Well, with the H version, the solder on the LCD's ribbon cable can sometimes crack and cause the white screen. I had this on one of my units.
You need to VERY carefully run a thin wire under the metal LCD frame to cut the double-sided tape BUT only at each side of the display - otherwise you will cut the ribbon cable!
You can then touch up the soldering connections.
There are photos of the H4's LCD cable on the forum's photo gallery to give you an idea.
As for the H4, I've never seen this - the the H4 uses a ribbon connector so make sure the tabs on the connector are pushed in properly.
Good luck