FWIW, I'm not as concerned about the humming sound as I am the burning smell. There should never be a burning smell. If you are confident of your ability to do the following, I would suggest it.
- Unplug shore power.
- Disconnect the battery(s).
- Remove the panel from the front of the fuse box / converter box. (Remove it - don't just open the door)
- Get a sturdy screwdriver, and tighten every screw that has a wire under it. Tighten them very firmly. Pay special attention to the screw that holds the black wire in each circuit breaker.
- At the same time, pay special attention to the screws that hold the white wires in the neutral bar, and the bare wires in the ground bar. (The ground and neutral bars look similar, but must not be electrically connected.)
- If you need a special screwdriver or wrench to tighten the heavy entry wires, get one.
- While you are looking in there, look for any scorch or burn marks. In addition, look for any corrosion. Everything in the box should be clean.
- Tell us the make and model of the converter. I'm betting it is a Magnetek / Parallax 6300-series.
- Button everything back up.
Do you have an electric jack? These have been known to damage the Magnetek converters.
Let us know what you find, and we'll go from there.
Bill