You don't have to worry about losing your favorites' list because I'm not asking you to replace IE with the new guy.

I'm asking you to install him
alongside IE.
When you install a 2nd web browser, these are the only things you need to be worried about, and
most secondary web browsers (including both Firefox and, last time I used it, Opera), will always politely ask you first rather than just doing it without your permission:
#1 - you need to make sure that IE remains your default browser if that's what you want it to be. [hide]What this means is that any applications which attempt to load a web page within the system's browser-of-choice will be using IE (as they currently do) and not the new guy. For example ...
- if you double-click on a .html file in your computer's hard drive, IE is what opens it now. It
could be switched to the new guy if you wanted it to be. So when it asks you, just tell it "No thanks, keep IE as #1."
- if a commercial CD-ROM has a java applet with a clickable region, and if that clickable region is supposed to ordinarily launch the web browser and load up the corporate home page, right now it's IE that does that for you. Again, you could alter this, or you could not, and it's all up to you. Don't want Firefox to be the new king of the hill? It doesn't have to be: it asks you, "Firefox has noticed that it is not the default browser. Would you like to make it the default browser?" And you usually have the three options to pick from of "Yes," "Not Right Now," and "No, and Never Ask Me Again."[/hide]
#2 - when it asks you, "Do you want to migrate your bookmarks from Internet Explorer to [it]?", you need to answer accordingly. [hide]
I can't guarantee it, but I'm preeeeeeeeetty sure that they DUPLICATE the list. In other words, you shouldn't have to worry about Firefox
deleting IE's favorites as it moves 'em over to Firefox. But if you're worried about it, maybe do a Google search to see if it's a real concern? And there's always the other option of telling Firefox, "No thanks, stay virginal."[/hide]
That's about it. Otherwise, you should be able to run both browsers at the same time in order to diagnose your problem.
IE fails, Firefox works ------> something's wrong with IE or how the router is communicating, specifically, to IE.
Both fail ------------> something's wrong with the router or (universally) with Internet access privileges on your machine.
Both work ----------> yay, success, you're happy.