Have you ran the diagnostic utility for your modem? Perhaps the message means exactly what it says; Hardware Failure.
You could also check Device Manager to see if it's reporting a problem. New modems are now so cheap, they are replaceable at about £10-£11 for OEM units (PC World) or cheaper still if you want to wait and order via the internet.
As with all installs, backup any critical data before doing anything, but simply reinstalling Windows over itself, SHOULD leave all other data in tact. Whether it will solve any problems you may have, remains to be seen. Sometimes it's an excellent fix, other times, not so!