Viruses and other Nasties

My daughter was downloading music, and visiting who knows what sort of sites, and I've ended up with all kinds of pop ups and junk on my computer. Several say they are some sort of virus scan, some have X rated stuff, but they all open up with Internet Explorer. I always use Mozilla Firefox when seaching the web. Can I delete Internet Explorer from my computer, and not mess up anything else. I started to, but then a window opened up saying that it could effect a bunch of files, and Firefox was listed in those.

Help! I've already gone over the computer with the free Trend Micro scan, and I've added Spy bot that found a lot of stuff. During the spy bot scan new windows keep opening up recommending I download virus ranger, and a couple of other things. They don't give the option to cancel, though, so I've just been closing the window with the X in the corner.

Deb