Remember, your outlets operate on 110-VAC and your lights operate on your 12-VDC from your Coach batteries. This should explain why your outlets still have power while your lights have a problem.
I'm not sure what your white wire went to or which cabinet you are talking about or what old light you uninstalled?
I can tell you that there are no spare wires in an RV that are just hanging around so that could be a problem for you.
I can tell you that you should make sure your COACH battery is in good shape, has water in it and is fully charged. When this battery voltage drops your lights and some other electrical equipment in your RV can start acting strange.
Without more detail, I cannot help you much more than this.