Are your spybots (Spybot, AdAware) both up to date? What version of Windows are you running? I've no idea what that hpccmd thing is. A long shot to try but won't hurt you by trying is looking in Add/Remove programs in the control panel and uninstalling anything suspicious in there. After that, also run "msconfig" from Start > Run, go to the Startup tab, and untick any startup items there you're not sure what they do, though you want to be careful since some things like nvidia/ati goodies might look cryptic while other viruses etc. pretend to look like other system things. Maybe post what you're unsure about here. You might find the hpccmd thing there too and can disable it.
Barely browsing the internet and not using the internet are completely different things - even using Internet Explorer just once is a security risk. You should consider replacing it with Mozilla or Firefox as soon as possible. Run Windows Update to patch known security holes. Even then, if you're running FFXI, you have an active internet connection during that whole time you're playing, so a web browser isn't the only possible way your machine can get attacked. Running a firewall helps this, even if it's the crappy default Windows XP one, since that's better than no protection at all. Firewalls that can check the actual programs running on your PC trying to access the internet are better though - such as Tiny or Kerio. ZoneAlarm does this too, but it's not a firewall I'd recommend or ever install on my PCs as it can also give headaches when that fails, even if Tiny/Kerio are more complicated to use.