The other common problems in computers as old as that would be leaking NiCad clock batteries (the corrosive gunk coming out of one of those will eat the copper

The other common problems in computers as old as that would be leaking NiCad clock batteries (the corrosive gunk coming out of one of those will eat the copper right off the motherboard), tantalum capacitors which like to fail shorted and burn out, and frozen bearings on disk drives. Modern machines may be more reliable because of the lack of moving parts, but they have other disadvantages in the longevity department. Lead free solder and conductive glue will start to fail after a few thousand thermal cycles. (Conductive glue is especially used to bond flex cables to LCD screens and is not something you could repair yourself.)