|"Since the power supply and graphics card worked in another computer, I knew those were not the culprit!"|
The above statement is not necessarily true.
To answer your question there is no real way to determine if those are the two choices other than testing the CPU in another compatible computer.
That said, IF there was some sort of power surge the first hardware to be affected is the power supply, then the board, then the CPU.
The power supply you are migrating for testing may not be suitable for your problem system for a number of reasons. There are variables beyond the graphics card.