Location relay switches on but will not rotate the engine to start

Do you know ?
*: ECM determines the start signal status by the signals of engine speed and battery voltage. The ECM activates the fuel pump for several seconds after the ignition switch is turned ON to improve engine start ability. If the ECM receives a engine speed signal from the crankshaft position sensor (POS) and camshaft position sensor (PHASE), it knows that the engine is rotating, and causes the pump to operate. If the engine speed signal is not received when the ignition switch is ON, the engine stalls. The ECM stops pump operation and prevents battery discharging, thereby improving safety. The ECM does not directly drive the fuel pump. It controls the ON/OFF fuel pump relay, which in turn controls the fuel pump.
The relay is located in the IPDE E/R under hood fuse / relay box . Should show location on inside of lid

It's not called a starter relay , it's theft deterrent relay and it's controlled by the theft deterrent module.
When the ignition switch is moved to the START position (and the theft deterrent module recognizes the key code), battery voltage is applied to starter solenoid (through the theft deterrent relay). Both solenoid windings are energized. The circuit through the pull-in winding is completed to ground through the starter motor. The windings work together magnetically to pull in and hold the plunger, which moves the shift lever. This action causes the starter drive assembly to rotate as it engages with the flywheel ring gear on the engine. At the same time, the plunger closes the solenoid switch contacts in the starter solenoid. Full battery voltage is applied directly to the starter motor, which cranks the engine.
Theft Deterrent Relay
Behind RH side of I/P, above I/P compartment

Check fuses #1 #2 #9 #10 #11 #12 in the battery junction box under the hood to make sure they are good

Check fuse #8 in the central fuse box inside the car

Not aware of a reset switch. Could be one of the ignition relays. Could be the crank sensor, camshaft sensor or the ignition module(coils) itself. If your engine has a distributor check that the rotor button rotates when you crank the engine. Any electrical gizmo's in the distributor should be checked also.

since you have been attacking the rotational mechanisms of the engine, I would have to assume that the problem you are facing is related to the turning over of the engine. Get a remote starter button and attach it directly to the starter and see if that get the starter rotating. If not then you are looking are either a bad power cable or starter solenoid. If so, the you are looking for a bad wire from the starter to the relay (or starter controller), a bad relay (or starter controller) or bad wire between steering column and relay. Check to see if there is voltage on one side of the relay socket (relay removed) when the key is switched to start position.

COMMON CAUSES OF NO-CRANK NO-START

Low battery (Check battery voltage, recharge if low, or jump start with another vehicle or battery charger).
Loose or corroded battery cables (Inspect, clean and tighten BOTH ends of BOTH battery cables).
Bad starter relay wiring connections or ground connection (Inspect, clean, tighten wiring connections).
Bad starter relay/solenoid (Check for voltage at relay, if relay has voltage but there is no "click" when key is turned to start, replace relay).
Bad starter (Jump battery voltage direct to starter to see if it spins, or remove starter and have it bench tested at auto parts store).
Damaged starter drive or teeth on flywheel (Remove starter and inspect drive gear and flywheel teeth, replace damaged parts if necessary).
Bad ignition switch (Check to see if voltage reaches starter relay/solenoid when turn to start. If not, check for open P/N switch and brake or clutch pedal switch. Replace ignition switch if defective).
Open P/N safety switch, or open Brake Pedal Safety Switch (automatic transmission) or open Clutch Pedal Switch (manual transmission). Bypass switch with jumper wire to see if engine cranks, or use test light or voltmeter to check for voltage passing through switch when ignition is turned to start.
Engine seized due to bearing failure or internal damage (Use socket and long handle to see if engine can be turned by hand, if not engine is locked up).
Engine hydrolocked due to coolant leak from leaky head gasket (Use socket and wrench to see if engine rotates, remove spark plugs and see if coolant comes out or engine can not be cranked with plugs out).

Things to check: Fuel pump pressure. The pump is powered through a relay. Verify the relay remains on while key is in the run position and engine starts and relay remains closed. If the relay opens, then the engine rotation sensor may be bad. This is part of the safety system to cease pumping fuel if the engine quits for any reason. Initially the fuel is pressurized and then while starting the relay remains closed and after aa short time if the engine isn't rotating fuel is shut off.

You're describing a no rotation issue and not a no start issue correct? If you dont hear/feel the starter relay clicking, it eliminates everything in the circuit to that point meaning the ignition switch, Transmission Range Sensor (TRS) (you don't have a neutral start switch unless you have a rare manual transmission), ground input from the Powertrain Control Module (PCM) to the starter relay coil, and starter relay are good. Based on what you've said that leaves the primary battery cable from the battery to the starter, and the wire from the starter relay to the starter solenoid contact on the starter. Have you checked their continuity? One more voltage to check at contact 30 (input volts from battery to starter relay contacts) on the starter relay socket. Should see 12vdc all the time.

You should check the battery. The true test is a load test. Does jumping the battery using jumper cables make any difference? If it starts, change the battery. I take it to check the starter you jumpered the solenoid contact on the starter to the battery correct? Have you tried wiggling the battery cables as you turn the key? They can corrode and fail internally. Are the engine and chassy ground connections clean and tight?

Try your inertia switch in the cargo area in back. Its located on the passenger side rear wheel well. Push the button.

I thing it is definitely the fuel relay. I had the same problem. The relay is quite big and it is located and bolted under the dash on the driver side, brown in color. You can't miss it.