The problem with IE is it's lack of security. Probably 99% of all malware is designed to take advantage of IE security flaws to get its way onto someone's system. Now, after 5-6 years of pretty regular patching on the part of Microsoft, it's gotten considerably better, but still not even close to where it should have been to begin with. A lot of times, all you have to do is merely visit some website for malware to be installed. You won't be asked if you want to install some ActiveX control or anything else. It's commonly referred to as a "drive by" installation. There have also been problems with IE where the site you see in the address bar isn't the site you're actually on. The new IE7 feature of the anti-phishing check has been proven to be completely worthless (it just takes too long for the list of sites to be updated). There have been numerous bugs which make it easy for someone to steal things like credit card numbers and passwords you enter into websites, even from secured connections. Microsoft also has a habit of sitting on certain security flaws, and not patching them for months, even years sometimes, if they ever get patched at all. The typical turnaround time for a security flaw in IE is around 2 weeks, while Firefox usually has a fix out within 2 days. And to the extremely literal of us out there, note that I said typical, meaning average, or sometimes its faster, sometimes its slower.
From what you've said now, I might think your Firefox profile was somehow corrupted. A fairly rare, but not unheard of problem. One that uninstalling and reinstalling won't fix.
In C:\Documents and Setting\<Your User Name>\Application Data there will be a Mozilla directory. Delete or rename it, then restart Firefox, which should force it to make a new profile. There are other ways to do this, I just find this method the most reliable.
If that doesn't fix it, then you've got something else on your system that's messing with Firefox. Something like some kind of web or download accelerator that I mentioned before, which may not have been fully tested with Firefox, and relies on some IE specific convention for doing things.