rip out the TCP/IP and Modem drivers and reinstall them. They could be damaged in some way. Very likely this happened as Windows is unstable that way.

Did you try pinging the gateway or DNS IP address? Not the host names, but the IP addresses. If this doesn't ping, chances are the ISP dropped the TCP/IP connection on you but left the modem connection open.

Also try from a DOS prompt:

IPCONFIG /RELEASE

IPCONFIG /RENEW

See if that repairs the connection.

As far as Virus scanning, you could copy small files you suspect are infected to a floppy disk and scan the floppy on a computer you know is not infected and has a Virus Scanner. Keep trying files until you find one that is infected or get tired of trying. Either that or take the hard drive out and mount it as a slave on another computer and scan it and don't otherwise access files on it from the primary hard drive. Once you have the hard drive on the other computer, you can copy whatever files you want to install on their hard drive.

A bad CD-ROM is a good indication that something is seriously wrong with the computer. Could be bad hardware. I've heard of software destroying CD-ROMs before, but thought it was rare. Slashdot had an article on Mandrake 9.1 destroying LG CD-ROMs. I had a friend who had a DVD-ROM shatter a disk for some reason and it put pieces of plastic and dust all over the drive. No reason for doing that, but he had been downloading all sorts of programs from Kazaa and had over 20 trojans I cleaned off his system. So maybe a Trojan did it?

I agree with Kmself, try Knoppix and see if you get the same problems there. If so, it is the ISP. If not, it is something wrong with Windows.

Edit: Cited the wrong person for Knoppix suggestion.