Hello and welcome to JustAnswer!
What you've seen with the cooling fan under the hood is normal. When you run any mix of defrost it runs the a/c compressor to dry the air, so the cooling fan under the hood will be running.
Your blower motor not running could be caused by a few things. The blower motor, ignition switch, wiring, or resistor are all the most common things. The most common and likely out of these would be the blower motor resistor. This is mounted to the bottom of the heater box on the passenger side with two 8mm screws. It's job is to step down the available current to the blower motor to give you the different speeds. When the resistor fails the most common symptoms are the blower motor only working on high or not working at all.
The resistor is cheap, easy to test and replace. If you have a voltmeter you can unplug the resistor and check for continuity between all terminals of the resistor. If you find any with an open circuit it's bad for sure. Beyond that you could do some basic testing with a meter or test light to make sure it's bad before replacing it.