2003 Crown Victoria air suspension pumps but will not vent......how to fix?

Heater in 2003 crown vic stays on always ???? Blower motor ? Air blowing out vent's all the time ? Blower motor speed control module .maybe ! If that is what your taking about . Can't turn blower motor off .

There may be several reasons for your issue. Check here for some of the most important: blower vents not switching
It could be an actuator(motor) that stopped working.

Here is a list of Crown Vic part:
List Blend Door Actuator 2003 Ford Crown Victoria Reilly Auto Parts

Here's an example of what may need to be done in a similar situation:
If you are handy, possibly buying a repair manual similar to this may help:

If it has air suspension. the air pump could be turning on. If it was idling slow, the A/C pump could reduce rpm if step-up circuit did not stabilize rpm. Lower rpm can mean lower voltage.

leak in the bags or check valve bad or stuck.

LEAK IN SYSTEM CHEAK ALL CONNECTIONS AND JOINTS FROM THE MAINE PUMP.

Air ride suspension basically works like this. you have a small air compressor and a sensor that connects between the rear axle and the under body Frame. When this sensor detects a load movement like more or less weight it turns on the air compressor to air up or opens a exhaust valve to let air out. most common problems with this system. broken or disconnected sensor. leak in the air lines between compressor and shocks. or a bad or weak compressor.

have someone or someone's stand on the back of the bumper then turn it back on and see if it will raise it up.

Sounds like the problem is in the air bag suspension, not the compressor. The air bags shouldn't be losing air when the car sits. The compressor adjusts the suspension level according to the load. The air bags have a valve similar to a blow up raft that allows air to pass through both ways. If when the car is running the compressor is constantly running and not turning off, the issue is within the air bags and/or the air line.

You probably have a leak in the system. Did "they" check the lines and air suspension? "They" probably disconnected the compressor to keep it from burning out from overuse. You need to fix the leak before reconnecting or the compressor will wear out very quickly.

Chances are the electronic/digital HVAC control unit is bad. This same problem happened to me and I had to replace the entire unit. The dealer wanted to charge $800 for just the part! After I freaked out on them, they found a used one for less than half. Sorry, but there's no easy fix here.