I have an oil furnace plenty of oil and power to everything, but the circulator will not work. It hums when I turn the t-stat up. I would like to repair it. I cannot afford to replace it today -- and pay emergency service prices.

I don't know what kind of coupler you have to connect the motor to the pump but it is possible that the problem is there.
Another possible is that something has lodged in the pump between the impeller and the side of the pump or maybe just the pump bearing is tight and needs some lubrication.

OIL furnace OR Boiler? A circulator is usually on a boiler. A blower is usually on a forced air furnace. No matter what the issue turn the electric off and oil the motor. Then rock the motor back and forth a few times. Then re energize the electric and see if the motor runs. If not then you will have to call for service.