I'll throw in my tuppence worth too, having suffered innumerable similar problems with a modem years ago.
Firstly am assuming it is an infernal
(read internal) modem. They use a COM port which exists in hardware form on the modem, but in software form as far as the PC is concerned.
Port assignments are set on the modem using jumpers, and the documentation that came with it will tell you how to identify the port number enabled.
Once you know this and are certain of it, then Spanner's directions are spot on. If there are more COM ports than you "know" you have, or even duplicates, delete them all (except COM1 & 2) and reboot. If still no joy, you can manually add the COM port which the modem is set to use. N.B. I found that in my case, even though the modem was not found by the "plug & play" scan at boot-up, if you run the "add new hardware wizard", the PC may pick up the modem where it missed it before. Strange but true
If still no joy, it could be something simple like the card is not quite seated properly in the expansion slot.
Hope you manage to resolve it one way or another. Best wishes.