I'm assuming you are saying the motor does spin, just not fast. Meat ball is right, if it wont spin at all, check the fuses.
First, put the switch on high, that bypasses the blower motor resistor array and should provide straight ground to the motor.
If the motor wont get up to speed, i'd suspect the motor. There is a way to test that, though its not super easy.
You need two jumper wires, and a spare battery or a long pair of jumper cables. Under the passenger foot well is the blower motor. You want a two pin connector. It should have a dark green and black/tan wires. Unplug that. Now you need to have your jumper cables hooked up to a vehicle battery, or two jumper wires and a spare battery. Hook one jumper wire to each pin on the blower motor the position for the dark green wire is positive, the black/tan wire is negative. It helps to mark the negative jumper wire with electrical tape. Make sure the two jumpers aren't touching each other in the connector. Then hook the positive jumper coming from the dark green wire to battery positive, and the other jumper wire to battery negative. The blower should come on full force. If not, the blower is bad. If it does come on full force, we will have to continue troubleshooting.
EDIT: Checking for voltage won't do anything, Chrysler is weird and makes things different from chevy and ford. The blower motor is supplied straight battery voltage, it doesn't pass through any resistor array. The blower motor ground is fed through either the selector switch or the blower motor resistors then the selector switch. All resistors will measure 0V no matter the setting chosen on the switch. Measuring for continuity to ground will also do nothing for you as this is a high power application, not a very low power sensor. Your meter could read just fine near 0 ohms (for the high setting), but when a load is applied it could be much too high a resistance to operate properly.