Well, it failed again Sunday afternoon, and I replced the old thermostat with the brand new one.  Guess what, it didn't work either.  I tried to program it, and got an error message.  I traced out the wiring, and could find nothing wrong. Based on information I got off the internet, I unplugged the wire from the middle unit to rear unit connection and tried hooking the theremostat up there, but no joy.  I finally gave up and got ready to come home, then it started working again.  I am giving up and taking it to Alliance next week.  I am beginning to suspect there is a problem with the control boards, and I don't have the expertice to tackle that.