First off. Windows 2000? That you keep up to date? I haven't seen Windows 2000 updates since.... 2005. Security? WTF?
For the love of dog, use something like VirtualBox or VMWare. Now!
Second, as a techie who has returned to college I deal with this a lot. Firefox has been hit or miss. Sometimes, I have HAD TO use IE. It's a bitch, cause I use Ubuntu. Nothing sucks more then having to keep a dual boot system (I used previously) or a VM around just for that one class that requires that you submit files via IE.
That said, I have had professors are usually very understanding of using browsers other than IE. For instance my Macroeconomics professor posted my short go by for playing his videos which seemed to only play in IE. I don't know why but they only played in IE, and I forced them to play with Firefox, Greasemonkey and FlashFix.
Other than that, I have seen problems with Blackboard and Etudes. It's usually hit or miss. Depends on the professor. My best luck has been with Moodle. I haven't had one class that has been problematic on Moodle.