That's a thermostat for a heat pump only, but you've got a gas furnace. That's part of your problem. I bet your AC kicks on when you put it on Heat instead of Emergency (it should if this thermostat is working correctly).

Does the fan kick on when you turn the fan switch from Auto to On? If so, try moving the white wire from W2 to E on the thermostat. Make sure you turn the power on the furnace off first so you don't blow the fuse when you're moving the wires around. Make sure you keep the thermostat set to emergency heat mode.

Failing that, you can try to replace the thermostat with something compatible.

If that still doesn't work, something else is going on.