Anti-theft problems

My car's an RS and it's equipped with keyless entry, and antitheft from the factory. Very recently my remote began working sporadically, making me think the battery was at fault, but it's been switched and it's still acting up. if i lock the car and let it sit for a while, when i come back to the car the remote doesn't unlock it, and my dash LED isn't blinking. If i manuall unlock with the key and get in the car, the alarm sounds, but only about 30 seconds or so later. I can turn the alarm off with the PASS key, but not with the remote when this happens. In addition, if i do not lock the car and i let it sit for a while, it won't start, but it's not a starter problem and it's not the PASS key. i get the car to start by locking and unlocking the car with the power doorlock button on the driver side and try again. when the car's failing to start, even though i have the door closed, the door open chime sounds rapidly when i turn the key. very rapidly. like a machine gun rapidly. i'd appreciate any help you guys can offer.

Jack

well i'm not gonna even try to act like I know what to do but when I had trouble with my keyless entry and alarm in my '97 I was told to check my body control module. Even though that wasn't the problem I did some tests on it and it helped narrow down what was wrong (turned out to be a short to ground for me). Good luck, I know alarm problems can be a HUGE pain