Fan control on thermostat is for the A/C Unit NOT furnace (Place FAN in Auto----otherwise A/C Fan may run when operating furnace)
Furnace fan is part of furnace function
Furnace needs good source of 12V DC power
Some furnace circuit boards have a 'check/verify' circuit that will not allow furnace function if 'Sail Switch' is still closed prior to fan operation.
Sail Switch should only close when fan is running up to speed.
Could also be lack of 12V DC to furnace (blown fuse, tripped on/off switch on furnace, circuit board issue, thermostat issue etc.)
What BRAND/MODEL is your furnace ?? (Info should be on data sheet in drawer, cabinet door, folder/info pack, on furnace)