why no heat from heater? a/c is working. is it a sensor or control problem?

there is a water control valve that shuts the flow of coolant to your heater core off when A/C is activated, sounds like the relay that controls that valve or the valve its self is faulty.

My daughters 03 Passat had the same problem and in HER car's case we got heat by just putting the re-circulating dial to circ or to no circ (I forgot which position, but it made a WORLD of difference). In her case there was (and still is) a flap that opens up the fresh air in, and it was stuck open. I remember someone coaching me over the phone, and I could see it stuck open with a little flashlight (way under the dash at the heater box assy). Sorry I can't be of any more help. VR Brian