If you have a power outage, was this PC connected / protected by any sort of surge suppressor or UPS / battery backup? I had a friend lose an SSD to a power blackout event. If it was browning out before you lost power, it could have damaged something if it wasn't protected. In that case, nearly anything in the PC could be suspect, although the power supply usually takes the brunt of it, followed by the motherboard.
And if you've tried swapping in a known-good power supply (and didn't forget to plug in any of the cables - did you get BOTH the 24-pin ATX, and the 4- or 8-pin ATX12V/EPS12V connector?), then the only conclusion is probably the motherboard, RAM, or CPU, with the motherboard most suspect. If you remove the RAM (all of it!), does it beep at you?
Also, do you have any sort of speaker / chirper attached to the SPKR 4-pin header on the board? If not, get one, it will help diagnose.
If you've got a known-good PSU, and removing the RAM doesn't make it beep when you attempt to POST, then either the motherboard or CPU is bad, and you can test that by swapping a known good one. Best to test the CPU by moving it into another known-good mobo, and test that way. There is, a small possibility that either of them could be "walking wounded", and damage the other part, should you test them. This can be tested, by having a pair of similar CPU and mobo, that are both known good, and try swapping them, and if your test rig no longer boots, then something was damaged by the components under test. In that case, both should be tossed / recycled.
Chances are, if you remove the RAM, no beeps from mobo, that the mobo is bad. (Still, possibility of putting in a new CPU and testing, if it works, it was the CPU.) It's fairly rare for a CPU to fail, though, even if the mobo is shorted.
I'll be frank, this could be a rabbit-hole of tech-support, and given the age of the system, pull the HDD or SSD, and replace the whole rig. (Save the working PSU.)
Oh, and if you remove all of the RAM, and have a speaker connected, and it DOES beep, then that generally means the RAM is bad, and the mobo and CPU are good, because it beeps in the process of POST if it doesn't have RAM available. So that means that the CPU has started to execute POST. Which is a sign of life for the components. Swap in some known-good RAM, and see if it boots, then.