The forced air unit for my central air and heat this last week has started making a high pitched sound when the unit is not on in either the heat or a/c mode. The fau works when the system is turned on but the sound is always there when the system is not operating.

If the system is not operating it is probably not the system that is at fault. You may take the front off the furnace off and try to listen to where the sound is coming from.