After use, fan keeps running and control panel not working

A sticking relay or a fault on the controller/timer circuit board. It is a repair shop job because microwave internals are potentially dangerous for the unskilled.
In practical terms unless the oven is something really special it would probably be cheaper to replace than repair.

It is probably safe to continue using if opening the door stops it and the food is still heating in the same times as before.

The microwave is not supposed to shut off if you have food in it. it is designed to stay running so you will not forget your popcorn.

The make & model number would be helpful. There are alot of veriables that might cause this to occur. How long was the MW in use (the unit might have been to hot and the safety engaged) keeping the fan on to cool it down. There could be an issue with with one of the door interlock switches. Depending on the engineering, the control board could have had a hickup via a over current & shut down to protect itself. During the cut out was the cavity light on when the door was open. was the display blank. If you unplugged the unit waited a minute & then plugged it back in, did it operate again. It is not a good idea to open the control panel up, if your do not understand how to do basic electrical troubleshooting.

If the fan seems to run even after the microwave had completed the cycle, then it is possible that the drive to the fan is having a time delay. Also it has to be made sure that the magnetron has been cut OFF power or else it is not a good situation. You will have to remove the control panel and check on the board, check the drive to the fan, since the processor cuts off the fan and magnetron at the same time the fan circuit must be traced. Look to the circuit after identifying the fan wiring and back check using a multimter if you are able to trace. If not take help as this can be harmful in case the microwave works till the fan cuts off. A faulty capacitor on the board can create this time delay.

If the cooling fan is not working, that would explain the shutdown problem. The function of the fan is to cool the magnetron down when it is warming or cooking the food, if the fan fails to run, the thermal fuse will detect heat rise causing a shutdown with in 5 seconds or more, the clicking suggest fan issues. I would recommend a whirlpool technician to go through the system.

mcdevito75 here, Sounds as though the control board could be faulty, check with any appliance repair center in your area.

Shorted switch in the door latch assembly.wihout the full model number I can't tell how to get to it, but usually one needs to remove top grille, remove screw holding the control panel, remove control panel. Good luck.

The circuit board is faulty. It should be covered under the warranty. Call GE or the place of purchase.

which fan? the exhaust fan or the control board cooling fan? the cooling fan is controlled by a thermostat just behind the control panel. it turns the fan to protect the board from overheating.