Been Getting BSOD Randomly for a Few Months...

Something is happening due to AVG. Uninstall AVG using AVG Remover. Use Microsoft Security Essentials as your antivirus with windows inbuilt firewall, and free MBAM as the on demand scanner.
Download, install and update those, and then run full system scans with both of them, one by one.

Free up the startup. Windows does not need any other program to auto start with it, but the auto start programs often conflicts and causes various problems including BSODs.

1. Click on the Start button
2. Type “msconfig (without quotes), click the resulting link. It will open the System Configuration window.
3. Select the “Startup” tab.
4. Deselect all items other than the antivirus.
5. Apply > OK
6. Accept then restart.

As Paul stated too, the zip you uploaded does not contain any crash dump.

Follow it: Dump Files - Configure Windows to Create on BSOD
Go to Option Two, Point 2. Download the .reg file and merge it in registry by double clicking it.

Now wait for another BSOD. When it occurred, search the .dmp files manually in the default path: C:\Windows\Minidump or %SystemRoot%\Minidump. See if the crash dump is recorded or not (hopefully it will be recorded).Post it following the Blue Screen of Death (BSOD) Posting Instructions.

Dont run any disc cleanup program before you upload another zip.

ThatCreeper said:

Whoa, I just got around to using AVG remover and it gave me a BSOD.

Post it following the Blue Screen of Death (BSOD) Posting Instructions.

Went to go do that, and this error popped up. Will this affect the files at all?

Edit: Hmm, I also didn't get any minidump files. Ugh, I think I may not have done that REG file tutorial before the BSOD... as I was in the process of firstly removing AVG. After the AVG BSOD, that's when I did the REG file tutorial. So, I'm guessing that I have to wait for another BSOD?

Try to remove AVG in safe mode, if not already done.

Then configure the BSOD recording and wait.

ThatCreeper said:

Do you mean, like, re-install it then go in safe mode and use the AVG remover again? Sorry if I wasn't too clear before.

If it is removed already, it is all ok :)

You need to merge the registry entry. Double click on the .reg file, and then click the merge button.

Yes, it is rightly done :) Now wait and observe. OK? :)