Before wiping your hard drive or some other radical idea, at least try this:
Go to Control Panel and "uninstall" the modem. Reboot, and maybe it will reload the drivers correctly if that was the problem.
If that didn't work, go to your "Connections" and copy off all the pertinent information. Then delete the "My Connection" or whatever the dialup is called. Then reboot and re-enter the information.
If none of these work, you might just try a new modem, available now for almost nothing, if not totally free,
For a Compaq? For a laptop? I'll bet selection is limited and not cheap.