There are several possiblities, ranging from faulty fan motor, open/short in wiring, faulty control module or relay.
If you can give me the year of your PT cruiser and size engine, plus whether it is a turbo or non-turbo, I can give you some specific information for testing.
We need to start with some basic checks.
Check fuse #12(highlighted in yellow) in the instrument panel fusebox:
Next, check fuse #5 in power distribution box in the engine compartment. Also, check the 2 fan relays in the power distribution box(all yellow highlighted). If you dont have a DVOM(digital voltmeter), you can swap the relays out with another one for testing purposes:
power distribution box location(near air cleaner and strut tower):
Replace fuses/relays as necessary.
If fuses and relays are ok, then check fan motor itself. If you have a DVOM, disconnect fan motor connector and test for 12v at connector. IF 12v present, then fan motor is bad.
If you dont have a voltmeter, then you can run jumper wires from the battery to the fan motor. If fan motor doesnt run with 12v battery source to it, then fan motor is bad.
If you fan motor runs with 12v source hooked to it, or if tested with DVOM, 12v not present, then further tests are needed. A diagnostic scanner will be needed to test the PCM(powertrain control module), and then test for open/short in wiring harness