Integrated or on a plug in card?[PCIMA} Seems like with a software failure In which case - Control Panel Network Connection and make new connection Or a Hardware failure - replace card or if integrated - the whole computer.
Have you ran a diagnostic check on the modem through Windows? If not, do this Open Device Manager and expand Modems Select your modem right click on it and select Properties Click the Diagnostic tab Click Query modem If there is a problem with it Windows will give you an error
Don't know about a laptop, but my desktop began to play up rather seriously, with error messages including a regular 'No Dial Tone'. If I pressed connect, then I usually got it working again. Tiscali sent me a new router, never had any connection problems since.