The cooling systems in these cars are terrible. Coolant reservoir cracking like you repaired is very common. While it's possible you could have a head gasket leak, the car would probably be running noticably bad if that was the case.
You definitely should flush out the entire coolant system. Not just drain the radiator, but a complete flush. You could also try flushing out the heater core again by itsself, but more than likely you will need to replace it to correct the no heat problem. Heater core clogging is also very common.
While you do need to pull the instrument panel to get to the heater core, it's really not that difficult on a taurus and something you might be able to do yourself (although you will need a helper to remove and reinstall the dash). You don't need to remove it completely, just pull it back far enough from the plenum to get at the heater core. | 
