dross

My 98 Forester's alarm has started going nuts at random intervals. The alarm goes on and off over and over again, in random bursts. I can re-lock it with the remote but then it starts up again. It can do this for a little while and then sometimes it decides it's not fun to do this anymore and just stops. This has started happening more and more frequently. Last night it happened at like 3:00am in the morning. I'm writing this on a very bad night's sleep... I went out and drove the car around a bit -- that didn't seem to help. I finally got the wise idea to just leave it unlocked, and that worked. Anyway, any thoughts on what's going on here? I just got a new radio installed but the alarm was definitely acting up before that time. I also happened to drain my battery the other day playing around with the new radio with the car off. I got a jump and now the car starts no problem. But perhaps that's my problem -- low battery? My battery is the original one from 98. Any ideas? Dave