2008 Chevy trailblazer want start.

copy and paste
https://www.700r4transmissionhq.com/chevy-hhr-bad-starter/

If starter won't crank the engine when problem is ongoing? Make sure battery has a full charge and connections all good. Jump the starter relay, pull the relay, use jumper wire on switch side of relay, left side in diagram, cavities for terminal 30 and 87. The starter motor should crank the engine, that starter fuse is hot all the time. If you try the jumper, make sure transmission is in park or neutral and parking brake is set. Vehicle can't move. If you have key in on position, where dash lights come on, when you use the jumper, depending on the problem, the vehicle may start and run. By using the jumper you are bypassing the control side of relaY. right side in diagram. There are several components involved on the control side of relay, ignition switch--bcm--ecm--neutral switch. You need to have it diagnosed properly. Have you tried cranking in neutral instead of park, when problem is ongoing?

85 & 86 are the control side of the relay , one should have battery voltage (85) the other (86) doesn't .86 is control from the PCM - engine computer . PCM supplys a ground to close contacts inside the relay sending battery voltage to the S terminal on the starter solenoid . If the PCM doesn't see a voltage signal fron the park neutral safety switch it won't energize the relay .
Circuit Description (ECM/PCM Controlled)
Moving the ignition switch to the START position sends a 12-volt signal to the engine control module (ECM)/powertrain control module (PCM) Crank Request circuit. The ECM/PCM verifies that the transmission is in the PARK or NEUTRAL position. With the transmission in Park, voltage flows through the Park/Neutral position switch and feeds the starter relay coil. The PCM then grounds the control circuit of the starter relay. When the starter relay is energized it allows battery positive voltage to the starter solenoid S terminal. On some vehicles the starter will continue to crank the engine with the key released until it starts or the crank command has timed out to prevent excessive heat build up in the starter circuitry or the ECM/PCM receives an engine run flag.

Hooking up a factory or professional scan tool to see where the crank signal is getting lost at would be the easiest way . You obviously don't know how this works .
Circuit Description
For ignition switch power modes refer to Body Control System Description and Operation. Once the ignition is placed in the Run/Crank position, the control circuit of the Run/Crank relay is grounded by the body control module (BCM). With the Run/Crank relay switch closed, battery positive voltage flows through it and on to the park/neutral position (PNP) switch. With the PNP switch in either the Park or Neutral position, battery positive voltage will flow to the starter relay coil supply voltage input terminal of the engine control module (ECM) and the coil side of the starter relay. Placing the ignition in the START position sends a message to the engine control module ECM requesting engine start. If the ECM has determined that the transmission is in Park or Neutral and theft is not active, it will ground the control circuit of the starter relay. Battery positive voltage will then flow through the switch side of the starter relay to the S terminal of the starter solenoid, cranking the engine.

Your best bet , take it to a qualified repair shop.

I'm just talking about seeing if the starter will crank the engine. Battery has a full charge, battery connections all good? Engine and chassis grounds all good? Unplug the starter relay in diagram, use jumper wire on switch side of relay, terminal 30 and 87, the starter motor should crank the engine, no need to use key. However if you have the key in the on position, just where the dash lites come on, the vehicle may start? If you try that make sure tranny is in park or neutral and parking brake is set. If it will crank with jumper but not w/o, have to check control side of relay for voltage and ground. The voltage comes from computer, the ground is chassis ground.
In the diagram, you can see the starter fuse.

Do you know if it is ECM/PCM or BCM controlled ?
Circuit Description (ECM/PCM Controlled)
Moving the ignition switch to the START position sends a 12-volt signal to the engine control module (ECM)/powertrain control module (PCM) Crank Request circuit. The ECM/PCM verifies that the transmission is in the PARK or NEUTRAL position. With the transmission in Park, voltage flows through the Park/Neutral position switch and feeds the starter relay coil. The PCM then grounds the control circuit of the starter relay. When the starter relay is energized it allows battery positive voltage to the starter solenoid S terminal. On some vehicles the starter will continue to crank the engine with the key released until it starts or the crank command has timed out to prevent excessive heat build up in the starter circuitry or the ECM/PCM receives an engine run flag.
Circuit Description (BCM Controlled)
Moving the ignition to the START position signals the body control module (BCM) that engine crank has been requested. The BCM verifies that theft is not active and sends a serial data message to the powertrain control module (PCM) requesting engine start. The BCM also energizes the RUN/CRANK RELAY. When the RUN/CRANK RELAY switch side closes, and the vehicle is in Park or Neutral or with the clutch is fully depressed, if equipped, supplies voltage to the starter relay coil. The PCM verifies the transmission is in Park or Neutral and the clutch is fully depressed, if equipped. The PCM will then ground the control circuit of the starter relay, closing the switch supplying voltage to the starter solenoid. On some vehicles the starter will continue to crank the engine with the key released until it starts of the crank command has timed out to prevent excessive heat build up in the starter circuitry or the PCM receives an engine run flag.

Free wiring diagrams here
http://www.bbbind.com/free_tsb.html Enter vehicle info. year , make , model and engine size . Under system click on engine ,then under subsystem click on starting . Click the search button ,then click the blue link .
If you look at the diagram you will see the ignition switch ,when in start it sends B+ voltage to the ECM/PCM or depending on which system or engine to the BCM . When it see's this input it will energize the starter relay located in the under hood fuse box. This happens if the control module in charge see's another input from the PNP- park neutral position sensor and if no anti-theft system problems .
Good luck !

Could be a number of thing's , can you do automotive electrical testing ? Do you know if starting is PCM / ECM controlled or BCM controlled ? Do you know what these are ? BCM - body control module , PCM/ECM - engine computer !
Moving the ignition switch to the START position sends a 12-volt signal to the engine control module (ECM)/powertrain control module (PCM) Crank Request circuit. The ECM/PCM verifies that the transmission is in the PARK or NEUTRAL position. With the transmission in Park, voltage flows through the Park/Neutral position switch and feeds the starter relay coil. The PCM then grounds the control circuit of the starter relay. When the starter relay is energized it allows battery positive voltage to the starter solenoid S terminal. On some vehicles the starter will continue to crank the engine with the key released until it starts or the crank command has timed out to prevent excessive heat build up in the starter circuitry or the ECM/PCM receives an engine run flag.
Circuit Description (BCM Controlled)
Moving the ignition to the START position signals the body control module (BCM) that engine crank has been requested. The BCM verifies that theft is not active and sends a serial data message to the powertrain control module (PCM) requesting engine start. The BCM also energizes the RUN/CRANK RELAY. When the RUN/CRANK RELAY switch side closes, and the vehicle is in Park or Neutral or with the clutch is fully depressed, if equipped, supplies voltage to the starter relay coil. The PCM verifies the transmission is in Park or Neutral and the clutch is fully depressed, if equipped. The PCM will then ground the control circuit of the starter relay, closing the switch supplying voltage to the starter solenoid. On some vehicles the starter will continue to crank the engine with the key released until it starts of the crank command has timed out to prevent excessive heat build up in the starter circuitry or the PCM receives an engine run flag.
Do you know what a park neutral safety switch is ? What do you mean key stuck in ignition ? Can't turn the key to off position , or you can an the key will not come out ?
Your best bet , take it to a qualified repair shop .

No, just one relay. You only get porew to the relay from the ignition when you try to start it. The ECM grounds the relay to let power go to the starter. Do a rest for the security. Ten minutes on, thirty seconds off. This should turn the security light off. There is also a relearn procedure. It is three times the reset. Don't try to start it until after you turn it off the third time.

With limited info I would say starter is at fault. That would would account for no boost from outside source and when turn key the volt meter goes to zero.

Is there a warning light , padlock an car symbol lit when it won't start ? I assume it has to be a bad starter? Every time i jump the car it starts up fine.??? It wouldn't be a starter then ! Have the charging system check out . Have a voltage drop test on the starter circuit done . Test from the starter relay . check out videos on youtube , but don't assume anything . Test , Test Test .

https://www.youtube.com/watch?v=WMXENKujYtc&t=6s

Starter Voltage Drop

VEHICLE RELAYS Testing from the relay base

Plus you need to know how the starter system works for the vehicle your trying to diagnose . I 'am a GM tech , Chevy , Cadillac , buick , GMC. Have access to GM factory repair info. Been to a lot of GM training school's . The computers on this vehicle have a lot to do with the starting of the vehicle ,PCM - engine computer , the ignition switch is a low voltage input to the BCM - body control module , which will send a message over the GMLAN serial data communication network to the PCM to energize the starter relay or crank relay .The PCM also has to see a voltage input coming from the transmission range selector switch , showing it's in park or neutral , has to have correct fuel enable password from the theft module etc...
Also it take's is a little corrosion , lose connetion , lower then normal circuit voltage for problem to happen .
Factory service repair manual discription

Moving the ignition switch to the start position signals the body control module (BCM) through discrete inputs from the ignition transducer that engine crank has been requested. The BCM verifies that theft is not active and sends a serial data message to the engine control module (ECM) requesting engine start. The ECM receives a ground signal from the park/neutral position (PNP) switch or a signal from the clutch pedal position sensor notifying that it is safe to start the engine. Ground G105 supplies ground for the CRNK relay coil. The starter relay coil control circuit is then supplied voltage by the ECM closing the switch in the starter relay suppling 12 volts from the CRNK fuse to terminal A of the starter. Ground is supplied to the starter solenoid through the engine block.

The first step in diagnosing a problem like this , hooking up factory scan tool , checking for DTC'S - diagnostic trouble code's , checking inputs to control modules that are in charge of starting the vehicle .

Testing an knowledge is the way to a fix , an testing cost $$$$$