My central air fan will not shut off. I've replaced the themostat and filter. Still continues to run. I have tried to switch it to cool or heat and neither comes on.

Your relay switch is stuck and needs replaced. My ac unit would do this all the time. Call a repairman to change this part out for you. In the meantime if you want the unit to stop running trip the breaker switch to keep it from running until it is fixed.