Ok, well "you" don't "think" it's the PSU, you don't think it's the GPU, you don't think it's the CPU, you don't think it's the memory either, so since you don't think it's anything other than the motherboard, replace the motherboard. I guess then you'll know if you were right about what it wasn't, since you didn't think it was any of those things but had no real basis at all for determining that any of them were actually good or not. Seem like you're not willing to entertain the idea that ANYTHING might be faulty, so IDK why anybody should bother going any further with this. Replace whatever you think it is because obviously you're not going to take any advice about anything that might potentially be the problem.
Truth is, it probably IS the motherboard, but in order to determine that you HAVE to eliminate EVERYTHING ELSE, because there are no tests to run that at the end you can say "ha, it's the motherboard", by testing the motherboard. You test everything else, and when nothing else turns out to be faulty, you replace the motherboard. So if that's what you want to do, just do it. Save a lot of time and energy if you're not going to go through the usual steps anyhow.
Besides which, if it won't let you flash the BIOS then it's likely there's something up with the BIOS ROM on that board anyhow.