It sounds very much like the Blue signal from your RGB input is getting lost at some point (seen this before on old 1084 monitors)...
Pretty certain it's just dry solder joints on the board as you say pressing on the back fixes this problem. You'll need to either (yourself or someone qualified) check & resolder the connector joints and any joints that the Blue signal takes on the circuit board and this should solve your problem...
Dry joints like these can be hard to spot (even with a magnifying glass) and can be very flaky in their time taken to show up when in use, sometimes they can cause problems immediately other times they can take ages to show up...
Best thing to do is check and resolder as many joints as you can on the RGB video input circuitry and you should have fixed this annoying wee problem...
PS:Check your cable first, as it could also be a bad connection in there on the Blue signal and the slight movement when pressing on the back with the cable connected could be just enough to either make or break this connection in the cable...
