It sounds like your A4000 has given up the ghost, most likely due to faulty capacitors on the motherboard. These are easily repaired. However, you haven't mentioned the battery condition. This would be the other component that would kill your computer. Also, how is the power supply? Do you have a spare you could test with?
I had my A4000 refurbed by Amiga France a few years ago, my problems weren't quite as severe as yours. Given the age of our computers they do need to have a bit of care to keep going.
