A stable and properly cooled CPU should be able to run all three Prime95 tests pretty much indefinitely. The small FFT test is the one that mostly stresses the CPU, so given what we know already and what Prime95 is saying I think a bad CPU is the most likely culprit here. I suggest you download and run the
Intel Processor Diagnostic tool and see what that says about your CPU. If you don't get a clean pass there then I think it's terminal.