Seemingly Random BSOD or Black Screen + Windows Failed Update

Sometimes I can run for up to around 6 hours without any of these happening, but when it does happen there are sure to be more to follow. Computer restarts offer a temporary fix. Audio always continues to play uninterrupted throughout any of these (Excluding BSOD, of course.)

Ranked in order of frequency (Most common at top):
-Random screen freeze (Usually while browsing the internet, never seems to happen in games.) When it unfreezes my cursor takes the shape of what it should when I hover over something, but it won't change back (Ex. Changes to the I symbol when it goes over the address bar, but keeps the shape no matter where I put the cursor.)
-Screen goes black and the "DVI NO SIGNAL" message appears on the screen, computer sounds to be running normally. It usually returns to normal after a few minutes, when I have the patience to wait. This happened once while I was away from the computer, so it wasn't triggered by an action of mine.
-Screen goes completely black, no messages, and it restarts. OR I get a BSOD. I was thinking that maybe the black screen is actually a BSOD that fails to show me the actual blue screen. They both create dump files.

In addition to these things, the Windows Update "Windows 7 Service Pack 1 for x64-based Systems (KB976932)" Has been failing to install since about 2 months before the crashing started. The error code is 80073712. All other updates install successfully, I was considering the possibility that these two problems are related somehow.

Thanks for reading and for any help that could be offered.
Dump Files below.

A Clean reinstall didn't work, still getting crashes just as frequently. Am I right in assuming that the piece of hardware causing this is my CPU? Judging by "GenuineIntel" and how often it says processor. If so, I might just buy a new one.

Code:

BugCheck 124, {0, fffffa80074ed8f8, 0, 0}

Probably caused by : GenuineIntel

Code:

1: kd> !errrec fffffa80074ed8f8
===============================================================================
Common Platform Error Record @ fffffa80074ed8f8
-------------------------------------------------------------------------------
Record Id     : 01ce7cb27efd3f45
Severity      : Fatal (1)
Length        : 928
Creator       : Microsoft
Notify Type   : Machine Check Exception
Timestamp     : 7/9/2013 14:42:31 (UTC)
Flags         : 0x00000002 PreviousError

===============================================================================
Section 0     : Processor Generic
-------------------------------------------------------------------------------
Descriptor    @ fffffa80074ed978
Section       @ fffffa80074eda50
Offset        : 344
Length        : 192
Flags         : 0x00000001 Primary
Severity      : Fatal

Proc. Type    : x86/x64
Instr. Set    : x64
Error Type    : BUS error
Operation     : Generic
Flags         : 0x00
Level         : 0
CPU Version   : 0x000000000001067a
Processor ID  : 0x0000000000000000

===============================================================================
Section 1     : x86/x64 Processor Specific
-------------------------------------------------------------------------------
Descriptor    @ fffffa80074ed9c0
Section       @ fffffa80074edb10
Offset        : 536
Length        : 128
Flags         : 0x00000000
Severity      : Fatal

Local APIC Id : 0x0000000000000000
CPU Id        : 7a 06 01 00 00 08 04 00 - bd e3 08 0c ff fb eb bf
                00 00 00 00 00 00 00 00 - 00 00 00 00 00 00 00 00
                00 00 00 00 00 00 00 00 - 00 00 00 00 00 00 00 00

Proc. Info 0  @ fffffa80074edb10

===============================================================================
Section 2     : x86/x64 MCA
-------------------------------------------------------------------------------
Descriptor    @ fffffa80074eda08
Section       @ fffffa80074edb90
Offset        : 664
Length        : 264
Flags         : 0x00000000
Severity      : Fatal

Error         : BUSL0_SRC_ERR_M_NOTIMEOUT_ERR (Proc 0 Bank 0)
  Status      : 0xf200004000000800

The first parameter or argument has the value of 0x0, which is a Machine Check Exception, which means the CPU has detected a hardware problem and the address points to a processor error because the CPU has found one, so it could be a different form of hardware which is causing the issue.

As a result, of the the black screens, then firstly I would stress testing the graphics card for any problems:

• Video Card - Stress Test with Furmark

What exactly should I be looking for? It runs pretty smoothly, getting up to around 93 degrees and leveling off, other than that nothing really happens.

Did you notice any artifacts or weird distortions? How long did you run the test for, and how long did it take for the temperature to reach 93*C?

I ran it for about 45 minutes this time without seeing any distortions or artifacts or anything out of the ordinary.
It hit 90°C at about 2 minutes (starting at 48°C) and increased very slowly, jumping and falling everywhere in the low 90s. At about 30 minutes it started jumping around anywhere between and including 93°C to 96°C. For the next 15 minutes it stayed pretty much the same.

I also thought it might be worth mentioning that the small clip at the end of the PCIe x16 slot is broken off, so the GPU is hanging sideways in its slot without anything but the actual connectors holding it there, so the card isn't completely perpendicular to the motherboard as a result. It dips a little bit. One card or another has been in there the same way without any problems for the past 3 years, however.
TL;DR: is it possible that my problem is caused by a bad connection? Maybe the connection has deteriorated over time?

The temperature rose very fast for such a short period of time, I would check for any overheating issues as well, open the case and then clean the fans and heatsinks with a can of compressed air.

I would definitely check the connection, have you tried placing the card in a different PCIe slot?

I sprayed everything, and the temperature holds at about 88°C, but it still hit that mark after about 2 minutes.
Unfortunately my motherboard only has one PCIe slot.
I also propped the GPU up with a coin, so hopefully it's closer to the way it's supposed to be plugged in.

Also, my screen froze earlier and I decided to try running furmark immediately after. The framerate was 4 instead of the usual 10 or 11, the temperature held at about 72°C, but what was most odd was that the GPU load was at 1%, instead of the usual 99%.

Strange, and does your motherboard or CPU have a onboard graphics card to switch to?