Why won't my heater fan come on?
If you tie the red and green together the fan should come on assuming the transformer wires are getting power (and it sounds like they are).  That's the only thing the thermostat does when you put it in "On" mode.  There shouldn't be and switches in the way.

The fan motor could have a start capacitor to kick it off, and those do go bad.  That's be what I would check next.  Also, the 24v current from the thermostat causes a relay to close which switches power to the fan.  Those relays can also go bad.  When the thermostat is turned to "On" mode, can you hear a click when you are right next to the blower (need a helper)?  All things to check...