My girlfriends PT cruiser was making a sort of whirring sound (like a fan, but the fan was not on). The sound even continued after turning the car off. Like. Completely. Key in my hand.

Sounds like it's the radiator fan. When they're on their way out, they begin to seize up and make noise. That's also why you still heard the noise after the key was in your hand. Fans continue to run after car is off. Turn the car back on and get it up to operating temperature. Then turn on your A/C. Your cooling fans should kick on. Pull over and lift the hood and see if it makes noise while running. If you know where the ECT is located, unplug the wire harness from it, that should make your fans kick on. If not, just take it for a spin and turn on your A/C.

It won't even turn over. And I checked the fan and it wasn't on at all.

The car won't turn over now? I would start by checking your fuses and relays to see which one is blown. Check your positive battery cable from the battery to the starter. See if you find any melted wires. Did this all happen when your tried to start it, or did all this noise happen while driving? If this happened during start up, it sounds like your starter may have been stuck causing it to overheat. If this is the case, check your fuse and relay for the starter.

Reelin68 is absolutely correct, I might add that the fan is made of plastic and most of the components are as well, the motor that runs that fan is integral to the engine. Fuses and wiring are all connected. I believe the fuses in the PT are color coded and the ribbon that shows that it is blown is on the top of the fuse itself. There are fuses inside the car and outside under the hood. Check them all.....Good Luck