My central air fan does not stop running unless power is switched off at the main electrical breaker. Could it be the thermostat? What steps to do to find problem? Help

First make sure the "Fan" switch on the thermostat is turned to "Auto" and not to "On" - which will make it run continuously. If that's not the case, then the control board may have a stuck relay. Try flipping the thermostat fan switch quickly from "on" to "auto" several times (leave it on "auto") and see if that helps. Is the unit cooling okay? If the compressor is running the whole time and not cycling on & off - or the unit isn't cooling properly, you may have deeper problems - low freon, bad compressor, etc. If the simple solutions I mention don't help, call a service technician to diagnosis your system...

Are you talking about the inside blower motor fan or the outside condensing fan motor?

Thanks for the responses. I switched the breaker off and on a few times and it worked. Guess the relay sticks(18years old)Yes the air is cold. It's the inside blower motor.

I'm glad I was able to offer some help... It's likely the relay will stick again in the future - whether you opt to replace the control board or look into a new system is your call - but I personally wouldn't waste much $$$ on an 18 year old unit - you've probably gotten most of the 'goodie' out of that system...