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.)

The "Capacitor Plague"[1] almost guarantees that machines made 10 to 15 years ago will have shortened lifespans. Would be interesting to peek into the future and see what antique computer collecting is like and if a working 2002 machine would be more expensive because of its rarity.

[1] https://en.wikipedia.org/wiki/Capacitor_plague

This raises the philosophical question of where the life of the computer truly lies. Is it within the capacitor? Is it within the network of the individual parts?

If you replace the capacitor did you resurrect the dead or just fix a broken part? https://en.wikipedia.org/wiki/Ship_of_Theseus

Tangentially: anybody have an expectation on longevity of a 2015 machine with decent components vs. one from that era? Are 2015 capacitors still as troublesome? I expect having fewer moving parts (as well as there just being fewer separate (visible) parts in general!) probably will help modern machines last longer.

You're probably right, but replacing them would be many hours of work, and there doesn't seem much point. I was mainly interested in seeing what I'd left on the hard drive :-)

My 486 machine was also dead, but I pulled out the drive and managed to find an old IDE interface on a 10 year old computer that would read it (after trying several), and copied it. (Turns out there was nothing interesting there.) The old disk drive was the only piece of old equipment I could get to work.