The fact that it crashes more when under load leads me to believe it is PSU but I am just guessing here.
Yes, you are guessing.Replacing every component is a very costly way to troubleshoot.
Try this, not because it is likely, but because it cost only your time. :
Disable the floppy dive floppy drive. No power, not data.
Do the same for the DVD drive.
Use just one stick of RAM
Remove nay USB devices not needed for basic use.
Disable any and all wireless devices. Radio off. No wireless mouse or keyboard.
As stated, it is not lively, but it cost nothing to try.
More likely is a component failure in the motherboard. But a new motherboard is going to be a pricey test if it turns out to be a bad DVD drive. Or RAM. So fist eliminate things that would let the system nun anyway. Try both sticks of RAM, one at a time.