How To Check GM 1995 Anti-Theft Relay and Module?

Don't try to bypass it. Not a good idea. You need to clarify something for me though. When the car won't start, does it crank over normally? If you have a No Crank condition, you need to check the basics first. Battery, Voltage drop the battery cables, Ignition switch Signal to starter, Starter Relay, and Starter. If you have good signal on the purple wire to the starter everytime you hit the key but it won't crank, you need a starter. If you have no signal at all, it could be an anti-theft problem (is the security or other theft indicator light on or flashing when it won't start?) or even the transmission range switch, but most likely it is either the Starter relay, ignition switch or possible high resistance or a break in the wire. Try using a DVOM instead of a testlight. If you get voltage (greater than .5 V) on the purple wire at all, it is not the transmission range switch or anti-theft system. You can eliminate one test quickly. Remove the starter relay and replace it with another relay from the electrical box that has the same number on top of it and is in a system that you know works. If it still does the same thing, it is not the relay. Let me know the results of the tests I've given here.