I don't think you have to go any further to prove your fan has burnt out. It should come on as soon as you turn on the air-conditioning.
You can test the high speed relay (F) by swapping the relays around. The low speed is relay is bigger and if you have the relay marked SPARE (J), you can swap that around with it for a test. They are located in the engine compartment in the oblong box in front of the brake reservoir.
If your not mechanically inclined, a mechanic or worse ...(the dealer) will have to replace the fan for you. You can't buy the fan motor without buying the fan.
Here's diagram of the engine compartment fuse box. It's 180 degrees backwards from how it's under your hood but that's the way Chrysler printed it in the owners manual.
