The same thing happened to me about 6 months ago!
I have a 2004. The alarm went off randomly like twice a day for a week! Totally sucked.

So, I took the fuse associated with it, only
to find out it also diasabled my ability to lock the car (omg,duh!).

I Put the fuse back in a week later and it never happened again.

Weird. Didn't replace anything and was told I had a good battery.

Goodluck!