My intertherm model e2eb-010ha has been acting up. First it started with the heating element coming on by itself then cycling on and off, even with the blower off. Then I had trouble getting heat to come on, unless I banged on the circuit box in the unit, now the heat stays on even in ac mode. There is a broken black plastic piece with two metal rods in it and that has something to do with the problem, but is that the only issue?

"There is a broken black plastic piece with two metal rods in it and that has something to do with the problem, but is that the only issue?"
I'm not sure of what you are describing. Can you post a picture?
It sounds like you may have a sticking relay causing the electric heat to come/stay on.