The best I can conclude is that the modem in that PC is either not supported by the drivers on their site, it's a third party modem, or it's flat out broken.
Instead of guessing what device it is, lets try and actually figure out what it is and then we can hunt drivers down for that specific device.
Download something along the lines of Everest or anything else that will display information about your hardware. When you've found out what the device actually is, post here and I'll try and find the drivers for you, or, search for them on your own.