1995 Lumina randomly won't start about 30% of the time. I was told it might have something to do with the theft deterrent system. What do I do to check that out before going on to more costly diagnostics?

 

won't crank, I guess?

 

typically, the contacts in the ignition cylinder wear and change the resistance of the pellet resistor in the key.

Does the security indicator come on when it no starts?

 

Have the security system checked like he said above.
That is if it has that.

Also, does it crank weak? Maybe the starter is going bad?
Check it out is my guess...

I know older cars the wire ends and wire terminals rust on the starter causing bad contacts, thus causing weak start or no start sometimes.

My Beretta I had half the starter go intermittent, causing weak start and sometimes no start, I'd have to sit there playing with it till it caught...lol