UNIX for Dummies Questions & Answers

I am fully capable of reading a book to get the answers or looking to the web, but no one has the answer to this one. I had a Zoom 56K V34 Plus external modem (2836A) attached to my Unix box for about ten years without a flaw. This weekend I couldn't access the box remotely through the modem and onsite determined the modem was internally sick and buzzing with electrical failure. I have two used formerly working USR Sportster 56K 005686-03 modems as potential replacements. I have tried every which configuration of the DIP switches and been through the modem manager in Unix and can't fix my issue. The modem manager won't edit or auto detect the replacment modems, but the port shows to be configured for a modem @9600baud COM1 on tty1a. I have not changed anything in Unix, just checked things by following the books. I have however tried every suggested configuration on the modems and to no avail. The issue is the phone line is clear with a dial tone until I connect it to the modems (any of them including the Zoom 56K). If I connect the modem to the computer using the DB25 cable from before and the switch the power on the TR & CS (the other DIP sw config had the AA on) lights stay on then the TR light goes out for several seconds while Unix computer briefly seems to communicate to the modem without any input from me. I notice the TR light comes back on solid with some faint flashing of RD & SD on the modem. I have a way to monitor the line from the extension jack of the modem and within a brief time (seconds) after the "communication" between the machine and the modem the phone line will ring brief and play the recording for "your call did not go through as dialed...". The line will then eventually change to the fast busy and stay that way. When dialing in this weekend the recording for the "line was busy" was being played on the remote end and my 3rd party software would drop the connection. If I turn off the modem or unplug the line the dial tone is restored. This Unix machine has never dialed out in it's life and has no need to phone home anywhere. I only dial in to the machine and this has worked for a decade this way. This machine is otherwise isolated from the outside world and has no other means of connection. Would anyone here have some light to shed on my issue with the recent failure of my remote dial-in setup? It would be greatly appreciated. I am a fellow geek, but I do not normally play in Unix because it runs itself without intervention.