Is your dial-up one of the "pay per minute from any number" kind, or the "unlimited useage but from only one designated number" variety?

I ask because I had a problem with the latter type once. About 8 months after I moved house the service suddenly stopped working, I tried all sorts of things but eventually called the (expensive) helpline who told me I should be dialling from the number I had given up 8 months earlier.

For some reason their server(?) had suddenly decided to revert to the earlier number, I asked them to reset it to my current number, and all was lovely again within minutes.

I also once had a similar set of symptoms when it emerged that the ISP in question had gone bust, the service simply ended without warning.

Good luck!