1996 Pontiac Firebird, Security Problem, Please Help,

I got a 1996 Pontiac Firebird.
I lost my keys 6 months ago, and I had a brand new ignition put on.

In the last two weeks my car has issues starting. It's at completely random times, but the only consitant is after it's been sitting for more than a couple hours (like when I park it at night, and I go to start it the next morning) it always starts.

But after I take it out to work, etc, it is completely random.
It start, or it doesn't.

When it doesn't start you have to wait until the security light goes off (3 minutes), and then you can try again.
Sometimes it works, sometimes you just have to wait.

It's driving me crazy.
But I mean, it does start probablu 75% of the time, but I have to get this issue resolved.
The By Pass Method is not an option. I read about it, it's nothing I want to get into.

Thanks!
I also checked fuses, etc. They all seem to be ok.

Also.
I have a Master Key (without the chip) but it still starts the car (and the light stays on).
Sometimes it fails to start the car as well.

So I'm pretty sure the Key is fine ..
Please offer your knowledge, though.
I'm out of ideas ..