It could also be that the exchange end of your service has recently change, Pipex belonged to Tiscali and I think most Tiscali customers are being moved to TalkTalk equipment where possible. What exchange is it?
If so, an old modem may not be compatible with the new equipment, though perhaps updating its drivers might help.
As others have said, a new cheap (wireless) modem/router sounds a good idea.
My broadband basic info/help site - www.robertos.me.uk
My domains,website and mail hosting - Tsohost.
Internet connection - O2 Standard.