For the viruses : on a CLEAN computer, download either the Kaspersky rescue disk or the Avira rescue disk, burn the iso to a CD, then boot the infected machine from the CD and let the scanner do it's stuff. The Avira one is updated regularly (sometimes several times in a day) and does not need net access to get the latest virus signatures. I do not know if the same thing applies to the Kaspersky disk.
If your internet connection is still dodgy after cleaning your machine, you either have a problem with the router or your phone line or any internal wiring (phone line extensions).
This is where I start getting out of my depth a bit, but if it was me, I'd start by getting the phone company to check the line. If it was OK, I'd try connecting the router through the master phone socket. If things improve, the problem could well be with the internal wiring and I'd get someone to check that out. If the problem was still there, I'd be looking at changing the router.