I am not an electronics expert, and I've had zero training. That said, I've replaced a bunch of capacitors in loudspeaker crossovers, a Bose 901 equalizer, a CD player, a couple of dbx 118s, and so forth. I have a "project" where I'll be replacing electrolytic caps in four different GMT400 ('88--'98 GM pickups) HVAC dashboard controllers.
MOSTLY the problem capacitors are the electrolytics. They have a known service life of 20--30 years; (some sources say as little as 6 years!) and multiple ways they can fail. They can leak their electrolyte, which then corrodes the circuit board. They can drift out-of-spec, either the capacitance value, or the internal resistance, or both. And they can sometimes actually EXPLODE. Some years ago, the Chinese did some Industrial Espionage, tried to steal the electrolyte formulation from another capacitor company. They got it wrong, and caused widespread capacitor failure--the infamous Capacitor Plague.
https://en.wikipedia.org/wiki/Capacitor_plague
What you have look like Tantalum or dipped Ceramic caps, not electrolytic. I'm not saying they "can't" be defective, but the odds are against it.
Beyond replacing capacitors, I've fixed multiple electronic devices--remote controls, windshield wiper control boards, and lots of other stuff--by looking at the circuit board with a magnifying glass, and visually verifying the solder joints. Doing nothing more than re-flowing solder on various circuit boards has brought them "back to life". Sometimes I find a printed-circuit copper trace that's melted or cracked, so I solder-in a jumper wire across the break.
But doing that on a computer circuit-board seems unreasonably difficult. You'd spend entire days doing nothing but following circuit traces.