These things are nearly impossible to diagnose remotely, but if you have current, up-to-date antivirus software and have scanned for spyware/malware, you may be down to rebuilding. Although, a machine that old, I would seriously consider replacing (and not necessarily with a Mac

) before rebuilding. One other thought, have you run a Scandisk to check for a slowly failing drive? It's not likely that it would only affect the browser (bad sectors?), but it's worth checking at that age.
I installed Windows 7 on my Dell laptop recently and the new hard drive I ordered was flaky (stay away from WD Scorpio Black

). I noticed the problems first in Chrome since browsers are always writing lots of small files to the drive. I replaced the bad WD drive with a Hitachi which is running well.
Speaking of old PCs, I just put in a new Dell Vostro "all in one" running Windows 7 for my mom to replace her 5 year old computer running XP. I'm rebuilding the old XP machine and it's going to be relegated to the kids for their games.