What benny said, if you're also crashing during idle, then it may not be a CPU issue, have you considered the possibility of the RAM being slightly faulty? Run a ram tester like Memtest or windows own, (they're pretty decent either way).
A monitor losing signal is also a negative, it doesnt mean the CPU has "stopped" it usually means another issue is arising, -- Ram and CPU would usually cause lockups or slowdowns then an eventual BSOD, never monitor loss, Are you using onboard or Dedicated GPU? Have you tried updating your drivers?