Radio turns off when cranked

If your 2008 Polaris Trail Boss is not starting from the ignition switch but starts when you jump the solenoid, there are a few possible causes for this issue. Here are some troubleshooting steps you can follow:
1. Check the ignition switch: Even though you mentioned that you installed a new key switch, it's still worth verifying that the ignition switch is functioning correctly. Make sure it is properly connected and that the contacts inside the switch are not worn out or damaged.
2. Inspect the wiring: Examine the wiring harness connected to the ignition switch, solenoid, and starter. Look for any loose, corroded, or damaged wires that could be causing a poor connection or preventing the signal from reaching the solenoid when you turn the key to the "crank" position. Repair or replace any faulty wiring as necessary.
3. Test the solenoid: Even though you mentioned that the machine starts when you jump the solenoid, it's still worth testing the solenoid itself. Using a multimeter, check if the solenoid is receiving power when the key is turned to the "crank" position. If there is no power, the issue could be with the ignition switch, wiring, or a related component.
4. Verify the starter: Ensure that the starter motor is in good working condition. If the solenoid is receiving power, but the starter motor does not engage when you turn the key to the "crank" position, the starter motor itself may be faulty and need to be replaced.
5. Check the battery: A weak or discharged battery can also cause starting issues. Make sure the battery is fully charged and in good condition. Clean the battery terminals and ensure they are securely connected.
If you've followed these steps and are still experiencing difficulties, it may be helpful to consult a professional mechanic or a Polaris dealer who can diagnose and resolve the specific issue with your ATV.

Video below might help

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.

Bad starter or siezed engine...

Check battery for crank power and connection.

https://s27.postimg.org/yy2w2qx43/starter_motor.jpg

Click on the link.
Are you talking about starter motor? In the diagram, see starter relay, unplug the relay, see terminal 30 and terminal 87, if you use jumper wire between those two terminals, the starter motor should crank, Terminal 30 is hot all the time. If you try this make sure tranny is in park or neutral and parking brake is set. If it cranks with the jumper, the problem is on control side of relay, ignition switch--neutral switch--or wiring circuit, somewhere. see crank fuse, use a test lite and voltage on crank fuse when problem is ongoing. I can only help with testing.

Could be the neutral safety switch or the starter solenoid.
You could try cranking it in neutral, or check the small wire on the starter solenoid for voltage when the key switch is in the start position.

If you have power in aux position(ex.)radio works but doesn't when you put the key in the start position,the ignition switch is bad,the contacts are warn out for starting/cranking&run positions,these are used everytime you start your car,but auxillary is ony used once in awhile(ex.)your sitting listening to music while waiting for someone to come,but if you do have radio in the run position,but no cranking/starting you could have a blown resistor on fire wall or fuse for ignition,or the starter has called it quits,good luck I don't know if the starter is clicking rapid or just one click or just no power not cranking or cranking a better description of everything that happens will make this alot easier

bushes in starter motor or sticking solinoir

Honestly, it sounds like a bad ignition coil. When they get corroded inside they will draw power on a scale much higher than anything else on the vehicle. It is a coil and it's job is to take a little power and make a lot of it. If it's only when the key is in the "run" position, that is likely the case. The only real difference between the two positions is that in the run position there is power being delivered to the ignition system. Good luck.

this look like a low battery and every time you try to crank your car it takes more power and kill the main power to the radio
solution # 2 the radio as 2 power wires one is always hot ( with current) and the other is connected to the ignition switch if you have replaced the radio those 2 wires maybe are connected backwards the one that goes to the switch is probably connected directly to the battery and the one is suppose to be always hot is probably connected to the switch if you have the original radio have your battery tested and if is ok then try get a haynes book at any auto parts for you car and try to follow the wire that is always hot normally is a yellow or orange wire
solution #3 this apply only if you car still have the original radio
turn your ignition switch to the on position but don't crank your car and turn your radio on select a radio station then turn your ignition key off and wait 3 minutes then turn your ignition switch on again with out cranking your car and the radio should be in the same radio station you select if this test pass then chances are is your battery getting low and if this test fail then the hot wire has a blow fuse look for the fuse inside the hook let me know what happend and good luck