If you're really serious about getting this machine running, you need a service manual. Here is a .pdf download manual:
The power switch is always suspect, and connections to the computer boards (usually referred to as control boards) can be loose or slightly oxidized. Power supply boards can have bad capacitors that dry out after a few years and can break down. If they're metal or electrolytic caps, look for leaking or being split open. They're usually cylyndrical metallic parts, with 2 or 3 soldered legs.
Aside from these general things to check, the service manual will show you where any fuses are, and basically everything.
Good luck to you, hope this helps, and thanks for using FixYa.