Windows 7: Regular BSOD problems, Page Fault In Nonpaged Area or STOP 0x000000F4

My 2 yr-old unmodified Windows 7 x64 HP computer (w/ AMD Athlon II x4 620 processor, 6 GB RAM, integrated Nvidia 9100 graphics) regularly crashes with a BSOD approximately five minutes after booting up. It doesn't matter if I'm running a graphics-intensive game, or if I'm not sitting at the computer - there's a BSOD and it restarts. I didn't install or remove any hardware before it started doing this. A week before, I backed it up with a new Seagate drive, and I added the Seagate backup software. I deleted the software but that naturally didn't help.

The computer runs fine in Safe mode with networking - I've been able to leave it on all night without problems.

I also tried memtestx86, manually removing each board of RAM, updating all the drivers I could, going back to an old video card driver, returning to the newest Nvidia driver, scanning for viruses, restoring the system to two different restore points (one of them lost the registration for the Webroot Antivirus, so the computer is temporarily unprotected), and I've downloaded a number of diagnostic tools. Still, it BSOD's after five minutes or less of running when run in Normal mode every single time.

Here's the latest report, and I've attached jcgriff's recommended attachment, though I'm not sure it ran properly in safe mode.

Problem signature:
Problem Event Name: BlueScreen
OS Version: 6.1.7601.2.1.0.768.3
Locale ID: 1033
Additional information about the problem:
BCCode: f4
BCP1: 0000000000000003
BCP2: FFFFFA8007B55060
BCP3: FFFFFA8007B55340
BCP4: FFFFF80002FCB510
OS Version: 6_1_7601
Service Pack: 1_0
Product: 768_1
Files that help describe the problem:
C:\Windows\Minidump\061312-20467-01.dmp
C:\Users\Deanne and Anthony\AppData\Local\Temp\WER-57689-0.sysdata.xml
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Thanks for the help

Run an sfc/scannow command in command prompt at boot. If errors are found, run it twice more with each scan followed by a reboot.
SFC /SCANNOW : Run in Command Prompt at Boot

You have driver verifier enabled, is that correct? If so, please disable it.

The following drivers need to be updated:

These drivers can be found by searching them in Google and then finding the associated software or driver. Finally, find the latest version of this driver or software and download and install it. Some of the drivers may also be found here (if the driver says 'Windows Update' simply make sure all Windows Updates are installed).

One of your dumps indicate that UCOREW64.SYS was the cause of the BSOD so make it a priority to update it. Also make sure that you have the latest BIOS installed.