And you find helpful folk but not a tv repair forum with hot solder irons all warmed up and ready to go to work.
Today's fans have a third or more wires for the speed detection so all I can offer is that you should put your Oscilloscope on that and see the pulses vary with fan speed. No pulses and what voltage would be your engineer's guide to what to do next.
Sorry but this is as far as I can go here. Remember it's not a TV repair shop here. So call it in and arrange for repair.
My Samsung HL67A750 has a check fan No. 3 message on the screen. I replaced fan No. 3 and still have the message. HELP!