I have that system. I also have two A/Cs. only the FRONT one will make the furnace furn. (Is that a word).
Also there is a switch on the furnace itself (outside behind the access panel) this switch does double duty as a circuit breaker.. There is also a fuse in the usual place (Fuse box).
Now you might (or not) hear a relay click likely a few seconds after you select HEAT mode with a temp setting at least 5 degrees above what it is, or more. The Temp sensor for this unit is not (As many think) the remote, it is part of the A/C grill (little yellow tit) so it's warmer up there than it is around your toes. I've had to put a fan on the dang thing to settle it down and make it behave on occasion.
Next: To see if it will work at all:
Press and hold the Furnace button till you hear a BEEP (2nd beep) This will take several seconds. The furnace should come on almost immed.
If that does not work remove the ceiling cover (intake grill, 4 screws, two are hidden by the filter) and look for some BLUE wires coming out of the control box.. If they are not connected, Then that's not what controls the furnace.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times