None of these suggestions really addresses the fact that the only thing that changed (apparently) was the studio desk. They are all good suggestions though.
So yes, going to balanced cables could be a good idea assuming that the gear feeding the monitors has balanced outputs. But the original problem could still be there.
It seems to me that if literally *nothing* changed except the desk, the problem could be the placement of the monitors in relation to other pieces of equipment. Or it could also be caused by how the cables and power wires are run. Power and audio cables should never run parallel, but cross at right angles. It is also possible that there is a power supply like a wall wart or lump in line near the audio cables now that wasn't there before. Or the speakers could be nearer a computer monitor or other source of interference.
Those are the areas I would look at first.