hmmm, doesn't sound good. if you haven't already, you may want to open it up to check the capacitors on the board. small round components. you're looking to make sure that none of them have started leaking. look for fuzzy dull looking solder pads and joints.
otherwise, give the rom chip a good push back into the socket.
you don't get any colours on the screen during the time the amiga doesn't boot do you?
