It is truly amazing how many people cannot connect due physical connection troubles. A very common scenario is the cleaning lady ran over the phone cord with a vacuum. My absolute worst modem day involved a bad phone-cord that I believed was still good. On PC's, people sometimes have trouble detecting their modems during set-up. A cold-reboot, including cutting AC Power during the shutdown part of the cycle, is sometimes helpful.
Some manufacturers require driver software installed prior to physical modem installation.
Some PnP modems are easier detected by physical removal, cold-reboot, physical installation of modem followed by a second cold reboot. This last described remedy can be helpful if a Win98 user mistakenly removed drivers installed in a previous version of Win95. Modem Device Drivers exist that connect reliably in the 48000 - 53333bps speeds. V.44 Data Compression makes dial-up look like it may indeed be around a few more years. Modems are compact, transportable and affordable.