I recommend going back to square 1. Remove connections to arduino, remove that 10K resistor (what's it for?), power the lcd with 5V from that UNO, adjust contrast until you can see blocks. If that all works, power the lcd with 3.3V and readjust contrast until you can see blocks.
If the above works, use the UNO and proper contrast for 5V supply and run an lcd sample code.