I've never heard a coil hum It is talking to you saying something is goofy, I think
Is your ECU a 4 pin or 5 pin?
What test device are you using?
If it is a volt ohm meter what is your battery voltage with nothing turned on and what is it with the key turned on to the run position and then in the start position?
You can fix this, it is something, wiring, that is not connected correctly