This happened to me when I had the LCD cables connected 180 degrees, Pin 1 was connected to pin 6.
I made a reversed the cable and the Display worked. My problem was the cable Key was inverted because of the Connector Key.
This is shown in images below. On the BigTree and RepRap LCD controllers the Keyed connector is reversed.
[attachment 114080 BigTree.jpg]
[attachment 114079 Both-50.jpg]
This caused my display to have hte exact same problem as you as inquiring about.
I made a reversed the cable and the Display worked. My problem was the cable Key was inverted because of the Connector Key.
This is shown in images below. On the BigTree and RepRap LCD controllers the Keyed connector is reversed.
[attachment 114080 BigTree.jpg]
[attachment 114079 Both-50.jpg]
This caused my display to have hte exact same problem as you as inquiring about.