I have a similar problem with my 95 Cavalier except that it never had an alarm. I then replaced the engine and tranny from a wrecked 98 and now the car starts but stops and the theft light flashes. I do not know if it something with the computer or just the engine.
Either way I found this website when researching it.
http://www.passlock1.com/ the other address for it is "bypassmodules.com"
Never tried it but it may be what your looking for.
David.