Techie help needed please, IE, viruses???

I have my daughters computer here. She's having problems and was hoping that I could clean it up for her. I suspect that a virus has attacked IE. I was hoping that I could connect via my cable connection, clean it up, buff it up and load Mozilla, but that didn't happen. Here is what she told me and what I've found.

It's running slow, locking up, etc.
Will not connect to her dial up Juno
Will not connect through my cable modem, the connection is good but the interent won't open
It's a Compaq E-machine just over a year old.
No updated virus protection, only the original Norton
No Ad-Aware, Spybot, ect,

I only have one cable connection and have to replace my modem with hers to try to connect. I do have a second setup where I can set up her tower and work on it without cable or dial up connection.

Is there anything I can do without having to wipe out the whole thing and start from scratch? Any suggestions are very much appreciated. Please keep in mind that while I can find my way around a computer nicely, all the techie mumbo jumbo is way over my head :( .