Your car is turned off its the engine cooling fan which must be on.. It gets started automatically when the car engine gets all heated up.. It runs on the car battery even if the car is shut off and makes similar noise as the car is on..
how old is the car?...if its a rust bucket then its probably developed a fault in the ignition!
The timing needs to be adjusted , it has one is called "run on".
but how could she still drive it
Did you turn the key to off?