Swap the DIMM A (the one under the keyboard) with DIMM B (under the door at the bottom of the system.  Re-run the test.  If the error follows that module to DIMM B, replace the module.  If the other module fails when placed in socket A, the socket is bad - replace the mainboard.

I don't understand what you mean by the DIMM A, I only see a place for my battery, a place labeled M (which, I suppose, means mainboard), and a place labeled C (which I don't think means DIMM A) on the bottom of my laptop. I tried looking it up, and I think its my two processors? I'm not too sure.

Enlighten me please, teacher. x3

Note: It's booting up more consistently now, But its still not shutting down. Someone might also want to note that the booting up problem started after one of the Windows update (at the time of update installation on startup). Just if someone wanted to know/if that helps me in any way.

I had confused this system with the 1720 -- this one has both modules under the Memory (M) door.

Swap the two modules and re-test.  If the same DIMM fails in the other socket, it's bad - replace the DIMM.  If the OTHER module fails in the same socket the first one did, the mainboard is bad - replace that.

You have either a bad memory module or a bad memory socket.