Heater core might have some blockage in it, but unless you've neglected flushing the coolant for forever and a day I doubt that's the problem. It wouldnt hurt to change the thermostat. I'm not sure what you mean about the fluid 'not moving,' but make sure the level is full in the rad.

It's also possible there's a problem with the linkage that attaches the temperature selector on the panel to the heater control valve. If it came unhooked, the valve could've been left in the closed position not allowing hot water to come into the core (happened on my Honda once).