It's got to be something simple that we are overlooking. I still suspect a bad connection between the Arduino and the LCD so now it's time to get out the magnifying glass and check the solder connections on the LCD pins. Look for poor joints and for bridges (shorted pins).
The reversed backlight connections that seem to work OK still bother me as well.
Also, you never commented on this (from reply #3)
I am assuming that you can vary the intensity of the blocks from very dark to very light
Can you measure the voltage between GND and pin 2 as well as between GND and pin 3?
Don