There's defo 1A battery fuse on the board???.
Follow the battery leads back to the board and you can't miss it,test it.
Have you heard the bell box ringing at all?,infact have you ever tested the bells?.
That panel is around 17 years old so it's overdue a meeting with mr bin,besides even if the battery fuse was intact it wouldn't be acting in the way you describe.
e manno
November 2013