We moved into a new house. I installed a new Hunter Thermostat. I have a furnace only and the old thermostat only had 3 wires connected. SO I connected those three wires (G, RH and W/B). The heating system is working fine, except that when the heater is not engaged and I turn the fan switch to ON the fan does not come on. It will only come on when the furnace is on. Why can't I turn the fan on independently?
You haven't provided a whole lot of information, such as if the fan worked with the old thermostat. Regardless, I can help diagnose the problem.
The wires involved are:
Don't make any assumptions on wiring. You need to open the furnace, find where on the control board the thermostat wire is attached, and verify its wires are connected as you expect. If the wires look right, and your thermostat wiring matches, it's possible there is a break in the wire.
To check for a break in the wire, you can connect terminal R to G on the control board itself. I highly recommend turning the entire furnace power off while connect wires to the control board -- shorting something out can mean frying the board. If the fan powers up, then the board is good, and you need to find where the thermostat wire is damaged (or replace it entirely).
If the fan doesn't power up with the R and G terminals connected directly, then there is a problem with the control board itself, which most likely means replacing the board, unless you can diagnose and solve it yourself.