Here is a troubleshooting manual for the 5-button thermostats:
According to this, the thermostat's 4-wire cable should go to the first A/C, then the first A/C's second cable should go to the second A/C. I don't know what the second cable on the second A/C does. The furnace is hooked to the front unit. Note this is the example in the manual, if your Zone 1 was the living area and zone 2 was the BR, and furnace came on in Zone 1 then your coach should be hooked up this way.
If your coach has a 3rd zone then from the second A/C should go to the third A/C. If the 3 A/C's have two phone cables then I still don't know where it goes (of course there are coaches with 4 zones)
The manual shows you how to tell which unit is which zone and which should have a furnace by looking at the DIP switches (p5).
Also, according to the manual, the furnace is connected "to the two (2) blue wires from the control box" and does not use a phone plug. Perhaps one fell off or is broken?
It sure sounds like the cable from the thermostat is bad. Maybe try disconnecting the other A/C's connectors other than zone 1 and see if the it works?
Note the manual says they are not regular phone cables, the connectors are installed so pin 1 is pin 1 on the opposite end (with phone cables, pin 1 is pin 4 on the opposite end). If you can make or modify a phone cable (involves cutting one end or a cable and crimping another RJ11 jack on the cable) you can substitute a known-good cable between the thermostat and zone 1 A/C. You may be able to get crimpers and RJ11 jacks at Radio Shack, maybe even at Home Depot or similar store. There's a picture (Fig 2 on p4) that shows you how how the cable should look when you're done.
No problems with the long post, sorry for the even longer reply