System becomes unresponsive at random intervals, W7 64-bit

Let us know how that goes.

I believe I may have been a bit premature. I performed the memtest86 on the new RAM, for 7 passes, and nothing happened. I was running windows for a couple of hours, and everything was fine. But when I powered it on after performing some updates, it started freezing again. Is there a list of the updates that I should install, and what ones may cause a conflict like this?

Did you spec the RAM with absolute certainty? Run Crucial System Scanner software to find out what type of memory is in your computer to cross-check. I also google RAM Upgrade for the PC model to read all results to compare the specs given until I have it narrowed down several ways.

You asked about Updates? First check for BIOS update and read what it is for. Related?

Next look over these steps for getting a perfect Clean Reinstall - Factory OEM Windows 7 to compare how yours is done and maintained, because it compiles the best practices based on tens of thousands we've helped with here. If you have much variance in yours I would do a perfect baseline reinstall. Pay close attention to how drivers are to be handled in Win7 because it is the first driver-complete OS in the installer and via Windows Updates.

And, yes, you should have all important and Optional Updates installed at all times.