Progress Report: It's running Windows. Sound is working. Graphics card is working. I can even play music and movies.
I've found installation disks for all The Sims 2 packs* that I had installed, and Photoshop, so I can install all those tomorrow and maybe even test the machine's Internet connection.
Then I can try installing my old hard drive as a slave. If that works I can copy over all my files and I should be (mostly) back in business!
I still need to find the installation disks for Microsoft Office and see if I can find my license code for Web Drive, and then get everything configured before I can really say it's all working, but I'm getting closer!
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*I haven't find my original The Sims 2 disk but I have an unopened The Sims 2 Holiday Edition!
Added: And then on top of that, I did find my original The Sims 2 disk!