If you've taken out the simms and the cpu card and "cleaned" the connectors, then there is most likely another problem. Could it be possible that the power supply is the problem, showing it's age? My current A4000, with gfx card, has the weird situation of not booting unless there is a monitor plugged into the RGB port. Only started doing this in the last year or so. Maybe the hardware is just getting too old and things are breaking internally.
I hope you solve your problem.