I have had similar issues with LCDs on my sequencer build. This was down to the shield of the MIDI in socket being connected to ground. All was ok until I connected a MIDI cable to the PC via a midi interface, then strange things would happen. The LCDs would change brightness and sometimes flicker.
My MIDI sockets are diecast metal and fixed in a metal panel. The panel was connected to the supply ground.
The MIDI cable should only have a ground connection for MIDI outs, there should be no ground at a MIDI in. This includes the metal shield part of the plug. Most pre-made midi cables I have seen have the metal part of the plug connected to the cable shield and so will make a ground connection between the 2 pieces of equipment.
It is worth checking to see if the shield is making this ground loop.
There can be issues with switch mode power supplies where a difference in ground potential causes problems, again I had this with the sequencer. The solution was a radical piece of surgery to the power supply, I added an earth pin connection to the negative of the output. Before I added the earth connection the negative 0volt side of the power supply was at 98volts when compared to earth. This is pretty common, I have tested many SMPS and all that did not have an earth connection showed this type of potential difference between 0volts and earth.
Sorry for the long response but I hope it is of use.