First off, with it crashing like it is the last things i would think it'd be would be the video card and PSU. If the video card crashes, 9/10 times it doesn't crash the whole computer you just lose video, with the PSU, normally your PC doesn't get past the first Windows screen without it either shutting off or BSODing. Even replacing the case was a little extreme, however if it is still crashing due to overheating after replacing all of that, and you have made sure everything is plugged in you have 2 options. The cheapest would be to find a low priced, even cheap, cpu that is tested as working fine from say ebay that fits your socket and test the computer out that way. The other option is to look at replacing the motherboard, or at least testing it using the same method. Unfortunately there is no cheaper option, though tbh it does sound like it's definitely the cpu.