Judging from Carol's description, I'd guess that the software doesn't create an Internet connection -- it just dials into a service directly. Even if it does create an IP connection, it should work fine and override the Internet while it's connected.

The PC shouldn't be seeing a second modem at all in this situation -- the DSL is presented to it the same as any other local network connection.

If you look in Control Panel | Phone and Modem Options | Modems, what devices are listed in there? What's the exact text of the error message you get when you try to dial?

Finally, it might be worth unplugging the network cable from the PC, then rebooting and trying the software. I don't really expect this to work, but stranger things have happened.