Internet Explorer is required in order to download Microsoft updates (Windows, Office, etc), and to view certain sites which are not yet compatible with Firefox. Thus, you shouldn't remove IE from your system for an extended period of time.

From what you're describing, I think you might have a problem with spyware/viruses/trojans. Run full scans using an antivirus and an adware/spyware remover and see what turns up. (I recommend Avast Antivirus, SpyBot, Microsoft Antispyware, and AdAware...all free.)

Another possibility is that a program on your computer is trying to access the internet for some reason. I doubt it, as I'm assuming you're set Firefox as the default browser (so IE shouldn't be opening), but you may want to check any running programs anyways.

If none of this works and you want to try reinstalling Internet Explorer, click here for instructions when using Windows XP. If you have Windows 95/98/ME/2000 and are using IE6, click here for instructions on how to uninstall IE. Afterwards, make sure you redownload and install IE6 by clicking here.

Hope this helps,
John