If a consumer electronic device suddenly refuses to power on, it's a failed electrolytic capacitor most the time (in my experience). Finding them requires effectively no knowledge of circuits. Sometimes one is visibly deformed/exploded, but I usually just replace them all.

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.

I attempted to repair a coffee machine that had a short that left a black burn on the PCB. Replaced the parts around it and it still wouldn't turn on. Likely the power surge destroyed a lot of things.

Those sorts of power faults can burn out traces on the circuit board too (you can bypass the break sometimes), and often there are fuses that would n need changing (in my very limited experience).

Louis Rossman on YouTube has a lot of stuff on circuit repair that I find good, https://m.youtube.com/watch?v=_at9Jy3dfeY.

You can also test electrolytic in-circuit using an ESR meter. That's effective series resistance if I'm remembering correctly.

Imagine an industrial robot which welds gratings and its controller. Old. Manufacturer either long gone, or bought by another, and that merged construct merged again with another, ad infinitum. So no support anymore, no spare sparts. But the thing works O.K. has a comfortable display where you can program it easily in place, and even understands "teach in".

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.

That's the general idea, yeah. I always start with the power supply because that part is under the most electrical strain, and tends to get hot. That means its components are often both the first to fail, and the most likely to cause weird problems when they do fail. Other than that, it's just intuition about how I think the device probably works, and a lot of trial and error. Major bonus points if there's a datasheet available, or a kind forum poster has had a similar problem to give me a lead on where to look.

Faulty capacitors often bulge, so you can find them by visual inspection.

Bulge, or even just burst open and start leaking:

https://en.wikipedia.org/wiki/File:Al-Elko-bad-caps-Wiki-07-...