Need a way to remove Malware without downloading software

Okay, so because this economy sucks, I have no job, no money, and my own computer's broken. This means that to get Internet access, I go to the computer office of my apartment complex to use their computers. Trouble is, their computers are very dated (talking a 75GB HD, 496MB RAM, and an AMD Sempron 2800 processer on both systems they have for public use...oh, and their only browser is an old version of IE that doesn't even have tabbed browsing) and, from what an employee here told me, have NO virus protection software on them. Of course, they're set up so that you can't install any new software without admin approval. It gets exceedingly frustrating when the browser crashes just from simple flash banner ads when I'm checking my email or something. I can't load half the pages I need to when looking for jobs or other information or something. Is there some in-browser application or something that will scan these systems and remove malware, or do I just need to keep complaining to the staff?