2002 Pontiac Firebird Will not engage starter

Welcome to the forum, does the theft/security lite, stay on or flashing, when trying to start? Next, I'd check the circuits at the starter relay in the underhood fuse box. Voltage the load side of relay, terminal 30, is hot all the time. Voltage to the coil side of relay, terminal 85, goes hot with the key in the start position. Use a dmm to check for voltage.

The pcm grounds the coil side of relay, if no ground, I'd have to double check the security system.

Some of the national brand autostores will test the starter. Yeah, you have to take it off and take it to them. I'd still have to be sure the battery has a full charge and the connections are good.

If the security system is the problem, cranking the starter won't help. I can't help you bypass it.

When the starter refuses to crank, Is the purple wire at the starter solenoid, hot? You have to test when the problem is ongoing.

If voltage and ground circuits are ok. The purple wire and the starter field terminal is hot, when the starter refuses to crank. Either someting is putting a load on the engine and starter, in that case, if you had the lites on, key in the start position, the lites would react if starter circuit from switch is closed. Or the starter is faulty, don't care if you had it tested. Anymore the starter and solenoid is considered one unit. I guess I don't know how to help you, have a good day.