A machine-check exception is typically a hardware failure. If you're lucky, it's "just" a RAM failure and if you're super lucky, you can fix it by re-seating your RAM, or (lucky, but not super lucky) replacing a failing RAM card. If you're unlucky, it could be a motherboard problem.
On another Mac, create a bootable external drive (USB, FireWire, or Thunderbolt) with a clean install of a version of Mac OS X that you know your failing Mac supports, then plug that drive into the failing Mac and boot from that. If you still get the machine-check exception, you're probably seeing a hardware failure.