I had the exact same issue. My battery died on me while the alarm was activated. Manually opening the door produced the alarm (very loud!). I unplugged the battery and pulled the alarm fuse.

Upon installing a new battery and replacing the fuse, I tried restarting the car and also got everything to light up, but just got clicking. I closed the hood (previously I was leaving it open while I was reinstalling and testing), and it started right up! No problems since.

Try the easy stuff first: close all doors and lock car. Unlock, get in, close everything and try it. It's worth a shot before you go down another route.

Good luck!

Jeremy

P.S. If this works for you report back so future searches yield valuable results.