BC, can you document that?
The Capacitor problems in the aforementioned Macintosh computers are well documented. Anybody who spends two seconds with a web search can find loads of information on the problem(s). They exhibit themselves as issues with the screen, issues booting, issues with the sound, etc. That people can replace the capacitors and eliminate these problems seems to conclusively tell us the cause was the capacitors. Obvously if a PC was in a flood or got wet or dropped or something- then replacing the caps isn't going to fix the problem, and assuming that is in any way the sort of scenario to which I referred is dishonest at best- I'm not talking about every single problem, I'm referring to seemingly inexplicable issues or odd behaviour on older systems and motherboards. Of course they be caused by other things- for example the battery leaking onto the motherboard, which I specifically mentioned, and eating away traces and causing it to fail to boot, but lacking any other obvious damage, for a layman replacing the capacitors is as good a place as any to start if they want to try to fix it. In the OPs case I'd be more likely to check out the power supply and the power switch (and the reset switch) as a first step.
any PC over ten years old will have issues.
Come on now, you tell me to document something that takes a few moments to determine by consensus of those interested in that particular area, but then go and make a completely unsubstantiated, generalized, and easily falsified claim? I have an iMac G3 and an PowerMac G4 as well as a PowerMac G5 which are all over ten years old. They still work with no issues- so your statement is demonstrably false. Of course if the G3 for example couldn't keep track of the clock, I'm not going to go replacing the capacitors, I'd replace the battery (Which I did preventatively anyway). If it fails to boot and thinks there is no HDD, I'm not going to replace the capacitors then either. I was not suggesting that Capacitor replacement was *always* the best option. It's the best option when somebody really wants a system working again (for some reason) and there is no obvious cause, like a battery leaking all over the mainboard, or obvious corrosion from water exposure. Nobody is going to take a PC that melted in a house fire, was hit with a sledgehammer, or was on a sunken ship for 20 years, replace the caps, and have it working again.
Later systems with capacitors with the bad formula (Capacitor plague) also have well-known issues. These can be PC motherboards, add-on cards (though add-on cards tended not to use electrolytics) and of course things like game consoles (A Sega Game Gear with no sound (where the volume is turned up, obviously) is going to 99.9% of the time be capacitor problems, it's such a well-known issue and I've never heard of the replacement failing to resolve that issue. In general, replacing electrolytic Capacitors won't cover 100% of the problems with a typical PC motherboard, but they are the most accessible replacable component for somebody who isn't an electronics engineer.
For example- bulging capacitors near the CPU, and the system freezes, even at the BIOS, after 5 minutes. Do you think somebody should be desoldering SMD firmware EEPROMs and then comparing them to known-good copies online to verify they are correct? Should they be testing all the transistors on the board, one by one, trying to check which one failed? Or maybe they should spend 30 minutes to an hour replacing that set of caps near the CPU and see if that fixes the issue, and then move on from there if doesn't? it's not like replacing the capacitors is going to *cause* problems when done properly, and if somebody cannot replace capacitors properly I don't see what hope they would have for replacing a Surface Mount chip or other component even if they could identify it was the issue.
With older systems failures that don't exhibit any obvious error codes tend to be Capacitors. For vintage 5150,5160, and 5170 AT systems,
This shows that most failures were caused by a bad capacitor- EPROMs can go bad as
this user discovered therein, but most issues that are inconsistent or don't have an entirely clear problem component end up being capacitors. On the list there are 2 or 3 that were found to be the ROM-related, and in at least one of those cases, the problem was pretty well indicated by the quartz window of the EPROM chip being completely exposed.
Devices to test caps 'in place' are part of the radio-TV analog stuff. Trying to find a bad cap in a well populated PC board is near impossible. Unless you cut one leg of the cap out of the circuit. Too much work to be worthwhile.
Which is why you replace them all. It's a lot easier to desolder and replace a capacitor than desolder it to properly test the electrical series resistance. Then you have a set of known good electrolytics installed and if issues persist you can work forward (or not, depending on your skill level) knowing it is not caused by the capacitors. If somebody is willing to replace the caps on a system board from 2000 then I think the 5 bucks it costs to try it a problem.
On the topic of audio equipment which Salmon mentioned, I have a Denon Tape Deck which has electrolytic capacitors. It makes a clicking noise during playback. I won't be replacing the caps to try and fix it, because I was able to determine it was a gear missing a tooth. If it had weird volume issues, strange problems with the level meter, that sort of thing, I might consider the capacitors the problem but I wouldn't replace them because I'm the sort who tends to "butcher the board" with that sort of attempt anyway- (And because of the problem space of audio equipment, capacitors often are not responsible.
If a vendor gives you a five-year warranty on a motherboard, he will use components that he knows will last. Gigabyte does.
We aren't talking about systems made in the last 5 years, though. Pentium III boards are stretching back to 1999-2001 or thereabouts. Those 5-year warranties aren't particularly useful if they were provided at the time of purchase. Modern motherboards don't use many electrolytics and tend to use Surface mount tantalums which are more robust anyway, and the boards are now tightly packed enough that any sort of amateur board-level repair is usually off the table altogether.