Have a read through the threads in our Security forum for information on how to detect and remove spyware, trojans, etc.; such an infection could cause the behaviour you're seeing with IE.

I figured it must be a worm, adware or something of that nature. Any thoughts on how to stop it and fix the problem? The challenge is that when the computer is started in safe mode it opens and opens and opens. Not sure how to get to a spot that I can run virus/adware removers.

Do the IE windows ever stop opening? That is, does the system eventually stabilize enough for you to be able to run other programs?

If so, download Ad Aware, SpyBot Search & Destroy, and HijackThis (download links are in my signature below) on another computer (to avoid having to try to use the problematic IE on your compter), burn the programs to a CD, and install them on your system that way.

What is the URL of the page being opened? Is is about:blank? Is it your homepage? Is it a file on your computer?

It is IE itself. Once I log on to the computer, it starts to open on it's own and never stops. This happens even is safe mode.