Thanks, CP. I'm making the suggested changes now. I'm going a little overboard on the future-proofing here because I'm only home for the summer. (Going back to university in the fall.) If my neighbor wants an upgrade a couple months down the line, I'm not going to be around and they're not particularly tech savvy. Also, there isn't a computer store nearby that I would trust as far as I could throw them. The two in our area both ripped me off. They overcharge on all their service calls by as much as $60 + hardware costs.
EDIT: As for the sluggishness, I found a trojan in their tax software after I discovered that they were running without a firewall for over 2 months. I checked the system with avast!, but didn't find anything else, which makes me even more nervous. I suggested a partial manual backup with a reformat as the only method by which to be certain that their drives were clean. (They're very paranoid, and frankly if something did happen to them, like ID theft, they wouldn't even know who to call to report it.) That option got nixed when I found out they don't have a Win XP CD. I'm betting that they have an infection that has gone too far for it to be detected, much less cleaned up. Given the system's age (It has an AMD Sempron 3300+ with 512MB RAM, not really worth the trouble of upgrading) and state, they were the ones who suggested a new machine. And given that I don't want to spend my whose summer troubleshooting their hardware, this is the best option for everyone involved.
EDIT2: CP, I'm looking at the CPU you suggested, and I see that its FSB is only 800 MHz, but the motherboard's FSB is 1066 or 1333 MHz. Will that present a problem?