You got the fan to run so the T-Stat must be getting power?
But nothing works as in the OP. Only trouble I had with that was the slider setting to change the temperature the furnace comes on and shuts off got wonky. I had to keep setting it higher and higher to get the furnace to come on. You get a click. Had to get a new same type thermostat(Dometic)
Yours is a different brand, but the thing remains that they are sort of tricky.
1. 1991 Oakland 28DB Class C
on Ford E350-460-7.5 Gas EFI
Photo in Profile
2. 1991 Bighorn 9.5ft Truck Camper on 2003 Chev 2500HD 6.0 Gas
See Profile for Electronic set-ups for 1. and 2.