Chevy cavalier issues

I have a 1997 Chevy cavalier 4 door with the
2.2 in it. About 2 weeks ago, my "anti theft
system" light came on and my car would
occasionally start. A lot of times, I would
take the positive cable off, put it back on,
then the same with the negative. After
repeated tries it would eventually start,
sometime it'd take longer than others. Last
week we put in a new tumbler with new
keys, it started right up several times. But
then the light came on again. Contacted GM
and replaced the already new tumbler with
a GM tumbler and again, started right up.
Ran good for 2 days, then it messed up
again. I'm at a loss. We entered the right
codes, confirmed that process with GM.
Anyone know what might be the issue??
Please help! Even my papaw (a mechanic
for 50yrs+) is at a loss. Need help!