problem with LCD
since there are two different transformers ,there could be a ground potential difference.
And another reason could be the noise from the analog board.
what you can check is by,
1. Make a single transformer as the supply source.
or,if you still need 2 tranformers,
2. Instead of shorting both the grounds together directly, short it through a ferrite bead or by a low value inductor,say 470nF
3.Provide a capacitor very close to the Vcc pin of display to ground ,preferably a 10uF aluminium electrolytic caps.
check this and tell.
-cheers