I used to build PSUs (generic) for a company up in Chicago. And honestly I don't care what anyone else would tell you... you CANNOT leave them on continuously for months at a time.
I mean yes... sometimes it's good to leave your computer on, but not for months at a time. PSUs are not designed to do this. If they were, there would be no need for a power button on any computer. PSUs over time, like anything else except cheese and wine, will deteriorate and when this happens it causes your PSU to fluctuate voltages. The PSU can no longer hold a consistant voltage and "spikes" every now and then. Granted there have been plenty of cases where people have left their computers on for years at a time but I still hold true to what I said earlier. PSUs are NOT designed to do this. The more high tech PSUs become the better they are at handeling extended use but this is only an unintentional perk... not a feature! My theory as to what happened with your PC is that your PSU became unstable and poked your motherboard, hdd, memory, or whatever, in the wrong place. This would explain the issue of your PC still not working after a new PSU was installed. If I were you I would have someone with a volt meter or anything that can measure resistance, test your motherboard. That would be step 1... or if you can find a new motherboard, try it out. Then you would need to test your memory with Microsoft Memory Test (I think you can get that from Microsoft's website). I honestly don't think it's your memory though... but just to be on the safe side I would test it. If you've already tried a new HDD and the HDD seems to be fine then you can skip that. I'm willing to bet that the problem started with your PSU and bled to your motherboard. Good luck!