Unless the CPU was zapped by a high voltage surge, it's not defective because CPUs are tested very strictly and should work 100% reliably unless overclocked. OTOH memory modules aren't tested strictly at all, so try running at the actual rated speed of their chips, which is probably JEDEC profile #4, 1333 MHz, 9-9-9-24.
One person couldn't find errors with MemTest86/86+, but Gold Memory consistently reported a bad bit. It took about 76 minutes to find it the first time, but then another 9 hours passed before it was reported again.