The input for recording is automatic so when you turn up the gain to hear it, you are hearing the level of the monitor of what you are recording and not the recording level input. So, if it is not a bad cord used on the mic or something else (like a mic that went bad) or a cord to your monitor speakers or something like that, then the recording input must be too low to get a proper signal into the Babyface. If that is the problem, perhaps you need a Pre-amp for your microphone to boost the level up to get a proper recording. One way to tell is if the recording level into your DAW is high enough gain to make a good recording on the meter in that program. Or is the hum in the recording into the DAW?

May be a grounding problem on the cord, or another grounding problem somewhere perhaps with the screws too tight for the connecting cable into the Babyface, or somewhere else.

Other than that, someone else may have to help you on that problem.