BSOD soon after installing Windows 7 (64-bit) on Dell XPS 400

Recently I have been trying to upgrade one of our computers (Dell Dimension 9150/XPS 400) to Windows 7. While this Dell model is old, a brief search on the internet shows that several people have gotten Windows 7 to work on this model just fine, so I'm inclined to believe this should be doable.

I have performed multiple clean installs of Windows 7 Professional (64-bit) on this desktop, but inevitably I will eventually start getting a BSOD. When the computer restarts, I get the notification "Windows has recovered from an unexpected shutdown" with the following details:

Problem signature:
Problem Event Name: BlueScreen
OS Version: 6.1.7601.2.1.0.256.48
Locale ID: 1033
Additional information about the problem:
BCCode: 24
BCP1: 00000000001904FB
BCP2: FFFFF88002AFF318
BCP3: FFFFF88002AFEB70
BCP4: FFFFF800028EC185
OS Version: 6_1_7601
Service Pack: 1_0
Product: 256_1
Files that help describe the problem:
C:\Windows\Minidump\052112-24616-01.dmp
C:\Users\Cheryl\AppData\Local\Temp\WER-40014-0.sysdata.xml
Read our privacy statement online:
Windows 7 Privacy Statement - Microsoft Windows
If the online privacy statement is not available, please read our privacy statement offline:
C:\Windows\system32\en-US\erofflps.txt


Here are download links to the files that "help describe the problem":
Minidump file & Sysdata file

The BSOD is kind of a crap shoot; on some installs of Windows 7 it happens occasionally while on others it happens as soon as the desktop loads. The problem gets worse (or more likely to occur) the farther I progress in "setting up" the computer. Here is a general procedure I have been following:

1) Clean install of Windows 7 Professional (64 bit) on hardrive
2) Install all the Windows 7 Updates (the only drivers installed are those recommended via Windows Update as Dell offers none for this computer on Windows 7)
3) Install Microsoft Security Essentials
4) Install Microsoft Office Professional 2010
5) Install Microsoft Updates for Microsoft Office
6) Install other programs I need

One time I got all the way to step 6 and was ready to transfer backed up files to the desktop when I started getting a continual looping of the BSOD...with the most recent install, I only got to step 3 before the first BSOD occurred...

I have tried running CHKDSK but that does not find anything nor seem to prevent any problems. I ran a memory test via advanced setup (where you press F8 while the OS boots) and that said something like "Problems were detected...you will need to contact your hardware provider" or something to that effect. However, no specific information was revealed; perhaps a summary is supposed to come up once you reach your desktop but this was during an install where the BSOD was continually looping so I never could see the desktop for more than a few seconds.

Reinstalling the original Windows XP OS doesn't seem to fix the problem; regardless of OS, drivers, or other programs installed, the BSOD inevitably shows up and does not seem tied to a specific update, program, or action. I'm no expert, but I am inclinde to believe there is an issue with the hardrive and once the "bad part" of the hardrive starts being used, problems arise.

Any help or suggestions would be appreciated. If additional information is needed please let me know.