Regular BSOD - 0x50 - Page fault in nonpaged area

With Avast uninstalled, make a memory test. Test for 8 passes. Then test each stick in a good slot.
Guide to using Memtest86+ - Geeks to Go Forums

Alright, so after spending all afternoon getting another computer, downloading Memtest, and burning it to a disc, I now find out I can't boot from it.

When the computer is booting and I get the prompt to press F12 for boot menu, it completely ignores my prompts, as it does with any of the other ones (bios, system info, etc). Could the motherboard just be faulty? Could that be what's causing these problems to begin with?

A faulty MB could cause the memory problems. Your new BSOD reports show memory. Thats all that I can tell you at the present.

The reports usually give clues. The last few of yours were quite clear..Memory.

Code:

 Microsoft (R) Windows Debugger Version 6.11.0001.404 AMD64
Copyright (c) Microsoft Corporation. All rights reserved.

Loading Dump File [C:\Users\Richard\AppData\Local\Temp\Temp1_Seven Forums (2) (1).zip\Seven Forums\080312-13634-02.dmp]
Mini Kernel Dump File: Only registers and stack trace are available
Symbol search path is: SRV*c:\symbols*http://msdl.microsoft.com/download/symbols
Executable search path is: 
Windows 7 Kernel Version 7600 MP (4 procs) Free x64
Product: WinNt, suite: TerminalServer SingleUserTS
Built by: 7600.16385.amd64fre.win7_rtm.090713-1255
Machine Name:
Kernel base = 0xfffff800`0324a000 PsLoadedModuleList = 0xfffff800`03487e50
Debug session time: Fri Aug  3 05:43:19.521 2012 (GMT-4)
System Uptime: 0 days 0:06:49.832
Loading Kernel Symbols
...............................................................
................................................................
............
Loading User Symbols
Loading unloaded module list
......
*******************************************************************************
*                                                                             *
*                        Bugcheck Analysis                                    *
*                                                                             *
*******************************************************************************
Use !analyze -v to get detailed debugging information.
BugCheck 50, {fffff8a00a566000, 0, fffff80003580079, 0}

Could not read faulting driver name
Probably caused by : memory_corruption ( nt!MiCompressRelocations+70 )
Followup: MachineOwner
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Did you take each stick and test it in a slot for 6 passes?

Negative. The boot menu working caught me by surprise, and I had both sticks in at the time. I didn't want to risk shutting down to take one out and not be able to boot from the disc again when I start back up.

Does having both in simultaneously provide unreliable results? I assumed testing each stick in each slot was to figure out which stick/slot is causing the problem.

No. Sometimes testing all give false results. The test must be done the way that I said. I can, also tell you, I have never seen consistent bad memory results that were not correct. I can also tell you to press down hard on each stick, sometimes they are not set correctly.