System becomes unresponsive at random intervals, W7 64-bit

I did have both of the keys written down at one point. But recently I was the victim of a house fire, and a lot of important documents (including those keys) were destroyed.

Performing those steps did not give me a resolution. Just to be safe, I purchased a new hard drive, and reinstalled W7 on it. Nothing was wrong. I reinstalled MSE, and only then did I get the error again. I have since uninstalled it, and the machine has not become unresponsive since then. This indicates to me that it's likely an error with MSE and the current configuration of my machine that is causing the issue.

Try uninstalling MSE to see if problem persists, making sure Windows Defender turns on. You can replace it with Avast free edition if necessary.

Did you establish a Clean Boot, check the System resources listed, test the hardware from Troubleshooting Steps for Windows 7?

Even though it's an inferior install if you cannot find the key to activate you may need to order Toshiba Recovery Disks for your model which will self-activate, then Clean Up Factory Bloatware. If the problem persists after doing this or getting the superior Clean Reinstall - Factory OEM Windows 7 then it is most likely hardware-related.

The error has happened again. I'll be trying those options you suggested now and will report back with the results.

Let's also see a screenshot of Disk Management - Post a Screen Capture Image - Windows 7 Help Forums
to see if anything is obvious.

How closely did you stick with the steps to do a perfect install in Clean Reinstall - Factory OEM Windows 7?

If this is the still the HD which had GRUB on it then I would first wipe the HD with Diskpart Clean Command.

No, this is a brand new hard drive, and this is the first thing that I've done with it

I just got done following the tutorial to a T, save for the parts I didn't care about (like backing up the files and restoring them). But everything else was done identically and I am still receiving that error.

Have you tried running without MSE, using Defender or Avast to see the difference?

Test your RAM - Test with Memtest86+
for 5-6 passes or overnight. Swap RAM sticks, checking slots for debris, blow them out.

Complete any other steps missed from Troubleshooting Steps for Windows 7. Do you have a Clean Boot, are repeat errors resolved, all System Resources checked for problems and resolutions?

I have not tried running with something else yet. I ran memtest86 last night, and it worked for about 6 hours, and then it froze, but it didn't. It became unresponsive about 6 hours in. I couldn't reboot the machine using the keyboard, but on the screen, there was still a red + flashing in the title of the program. The timer however had stopped.

Then I would pull out the RAM sticks, reseat them after blowing dust out of their slots. Insert only one stick to test it individually, until you find which stick or slot is faulty. The tutorial shows how.

Thank you so much for all of your help. I tested each stick individually in each slot, and found that one of the slots was causing the errors. Because the RAM sticks weren't very large, I went out and bought a new one. And put it in the slot that didn't work.