I have experienced your same symptoms with my car (2005 CF Coupe) today with sound of electric motors runnung and car stops and won't start. This is the second time it has happened. I waited thirty minures until the fans no longer came on and the car started just fine. I did not have to disconnect the battery to reset it or anything. My theory is that the fans draw so much current (They sound like they are about to take off.) that the battery voltage drops below the level required to maintain the immobilizer circuitery and the car won't start. When the car cools down so the fans don't come on, the car can start and runs fine. I am looking for something in the fan circuit as the cause of the problem. Maybe the RCM solder joints need to be re-soldered?? When it stopped. The ignition lights worked but the car would not crank at all.

I have also previously had a separate problem in which the car will start for maybe 2 seconds and die. This happens three time then no longer will crank at all. This problem was caused by a key that was not being recognized by the halo ring in the ignition key slot. I went to the dealer and ordered a new key fob. Problem solved. The key security system is more complicated than necessary and one end up shooting ones self in the foot. The system has a Radio Frequency Identity (RFI) chip imbedded in the FOB. This chip requires no battery to be recognized by the halo ring in the ignition. The RFI is a static E-prom chip encoded with a unique serial number, ID number provided by the manufacturer. If this e-prom becomes unreadable or is damaged, your car will start 3 times for 2 seconds and them go into the immobilizer mode because since it didn't pass the RFI test you must be trying to steal the car and the system stops any further chance to start the car. The FOB also contains an IR powered electronic circuit which locks and unlocks the car. The third security feature is the key itself. The key will lock or unlock the door and turn on the ignition but will not
start the car unless the RFI chip is authorized by the Halo sensor around the key insert ring in the dash. If you have multiple car keys (FOBS) that work you are lucky. I do not.
If you get a new spare FOB, you will have to authorize the new FOB following a published procedure. Do not ever buy a spare used FOB off ebay because they will not work because they don't have the RFI chip programmed with the correct ID needed and there is no place to get that done.

I am not sure this helps anyone but the above facts are the result of my looking into the problem on my car. I am a 75 year old retired Military/Electronic Engineer/Computer Software Engineer. I love my Crossfire, it looks showroom new although it has 86,000 miles. Good luck.