Theft System Problem, new Radio 98 Sunfire

Hi, I installed a new JVC deck using a wiring harness adapter so I wouldn't have to cut any factory wires. About 4 days later, my car had the Theft System light on after a night in the garage and would turn over, but not start. I tried a few things I read about to fix the problem. I turned on the key, left it for 10mins and repeated 4 times. No go. Disconnected the battery for a hour. No go. I took the deck out and repeated both steps twice, no go. My very last try was to leave the key on overnight with the battery charger on. That worked. I was told the Theft System times out after a while and resets itself.
I reinstalled the deck and it ran for a day no prob, then the next morning, Theft light was on again.
My question is, will a simple bypass module solve my problem, as I was going to install a remote starter/ alarm anyway? FYI I guess my car doesn't have the chip in the key from the research I have done. Thanks

Guess nobody has that much experience on Passlock 1 here or anywhere. Anyway, gonna have to bite the bullet and go to the dealership. If anyone read this thread, I'll leave a update as to what happened.

I bought a new igntion cylinder. Installed it, the Theft light went from solid (which it always was) to flashing, I thought that was a good sign. Now it is the same as my old one, solid light and can't reset it by having the key on for 10mins X3 or unhooking the battery for 10 mins.