https://en.wikipedia.org/wiki/File:Al-Elko-bad-caps-Wiki-07-...
If that doesn't work, yea you pretty much start testing things with a multimeter starting from the power source. But if it isn't a capacitor failure, it's probably ESD or power-surge related damage and not worth trying to fix.
Louis Rossman on YouTube has a lot of stuff on circuit repair that I find good, https://m.youtube.com/watch?v=_at9Jy3dfeY.
But welding grates is more of a side gig of that company, so they only do batches from time to time. One day a new, rather large batch is due, but robot doesn't start up at all, and programmer stays dark. It has power but is dead. What to do? Disassembling the controller/programmer of course. Something super special, running only one "App", written in something esoteric, running on a CPU which was designed to only run that esoteric stuff and nothing else.
And probably a mouse somehow crawled into the case and shat and pissed onto the PCB, and the CPU. Which is corrosive and dissolves the pins of the CPU und the the copper traces of the PCB, turning them into some sort of gel. But not much area at all, so easy to bridge with wires if it weren't for the dissolved pins of the CPU. So i removed that part, cleaned it with compressed air, benzine and alcohol and then very slowly and carfully drilled open the edge of the CPU until i could see the bonding wires from die to pin. Again very carefully soldered wires onto the ones missing pins, bridged that over the broken copper traces on the PCB, hot glued that crazy work, and reassembled it.
Against my expectations it worked! At 10Mhz! For years afterwards. How the mouse made it into the case wasn't obvious because the largest openings had only the diameter of a pencil, and i can't imagine a mouse fitting through that. But it somehow did. Anyways, what i wanted to say is that sometimes you can see what's wrong without knowing electronics at all. Same with the capacitor problem other commenters mentioned. They have to have a flat top, any bulging is wrong, especially when the top cracked open and some gooey stuff leaked out. Or from below.
There is an extremely detailed article about it here: https://en.wikipedia.org/wiki/Capacitor_plague
They are mostly "refurbished" (=repaired and cleaned), and then sold again. If possible, even as new. Or, of course, sent back fixed.
I also spoke to someone from Russia who worked as a electronics repair person fixing things we would normally throw away because the price of new equipment is very high compared to the price of an expert's time to fix it.
This one's not on his channel but is a good example: https://www.youtube.com/watch?v=g0S1ku9xvDI