Won't stay running starts and then turns off right after it strats

With the issues you stated for starting, I'd have to check security system first. Can you check for trouble codes that relate to your security system? To check codes yourself, at the least, you need an obd2 code reader. When you changed the turn signal switch, you may have accidently caused a wiring issue?

I haven't looked at info/wiring for your security system, yet.

If this is the vats system, there is info all over the web about bypassing the pellet in the key. But, if the problem is somewhere else in the security system, bypassing that pellet won't help anything.

Anybody have any ideas, jump in, no problem.

Just to add, you don't have the vats, you have passlock security system, fuel injector disable.

Can you tell anything to point us at the security system. Is the security lamp on or flashing, anything? If security issue, there a relearn procedure that may or may not help?

Make sure the battery has a full charge. The procedure takes about 30 minutes or a little longer. Try to start vehicle, start and stall. Leave the key on, the security lamp should go off after about ten minutes. Turn key off 30 seconds and then do it again. The procedure 3-- 10 minutes. Hopefully after the last ten minute procedure, it will start.

It's possible that it isn't your security system?