Saturday morning I found that my heater was not kicking on when I turned up the thermostat. After fiddling with the thermostat, it finally came on and worked all day. In the evening I turned down the temp to 55 deg, and the heater didn't come on for the rest of the night. This morning (Sunday) my house was 48 deg. I fiddled with the thermostat the same way I had the morning before, and this did not work, even in the ON position. After turning everything off for a while, I turned the unit back on, set it to COOL and ON. The fan came on after about 10 min, but would not quit when turned OFF until I set it to AUTO. I then tried turning the heater back ON, and the fan never came on. The unit hums when turned on, but the fan hasn't worked almost all day. I am not sure what is wrong, but since the fan works sometimes I think something is going out. I have nothing to test the electrical currents with. What should I do?

Best guess would be your start run capacitor. It is usually located on the motor, looks like a small coke can or pack of cigarettes and has 4-5 wires connected to it. If you have never changed one you might want to have someone else to do it because you can get a big shock if you don't discharge it before removing the wires.