People often neglect to run thier modem phone lines through a surge protector and phone lines are subject to surges and lighning strikes, Modems often blow out due to this, the system dose not have to be on for them to get hit, so it quite possible to have 2, or even 3 bad modems in a house.
If you can plug in a single line phone and get dial tone, your modem should too.
In the control panel, under modmes, if you go to modem properites you should see a diagnostics tab, querry the modem, of you get response AT info and command list Like ATHO, the modem is usally ok.
As far as I know, a Comm port has to be installed for it to show in the modem comm port list. Creating a new comm port is tricly as you need free IRQ and IO addys, and if its not on your system chances are your UART dose not support the ports.
You can try swapping your system modems with known good ones to test.
You may also consider a wireless or wired Local Area Network and use Win 98 SE Internet connection sharing insead of 3 modems where only one system can be online at a time. Once system connects to the net and the others use it as a gateway.