No experience with Geek Squad, but 15 years of experience in IT. With corporate IT contracts, the people working in level 1 tech support are almost universally clueless. If they had much of a clue, they’d be working a higher level of tech support, or they’d not be working support at all. The folks at Geek Squad are likely to be even lower on the ladder than this.
That said, occasionally you’ll find a gifted person working the “low end” of tech support, Geek Squad, etc, someone with a passion for the field, quite knowledgable, and just trying to get their foot in the door. You’ll only get that if you’re very, very lucky.
So, the reason they’re advocating a reinstall is because that’s generally their primary course of action. They know that, barring a hardware problem, your machine will function after a reinstall. So they’re not going to spend time troubleshooting. If you do choose to troubleshoot, please post the details your “black screen of death” displays.
So in general, I wouldn’t trust them, or pay them to do pretty much anything. If they’re not even going to reinstall your apps, restore your backups, etc, don’t pay them $200. You can do this yourself. If you do want to reinstall, have a license key, but don’t have your original install media, you can call Microsoft and they will provide you with replacement media for a nominal fee, on the order of $10-20 US. However, Windows XP is currently under Extended Support until 2014. This means that the only updates you would receive from Windows Update will be security related, and not bugfixes, performance related improvements, etc. Only security-related bugs will be fixed.
A new machine is a good choice, you can get a machine that will blow away your current machine for a remarkably cheap price. It will come with Windows 7, which is far better than Vista IMHO, and you’ve already got backups of your data.
Anyway, I’ve rambled enough, last thing I’ll say is, you mentioned a few Antivirus packages. I can’t recommend NOD32 enough. It places pretty much no performance hit on your machine ever, and has never missed a virus “in the wild”. I’ve been happily using it as a “set it and forget it” virus software for a while now, have had zero infections, and I’m known to download from some fairly shady sources. It’s from http://www.eset.com/