I have a simple script based on Hello World connecting an Arduino R3 to a standard 16x2 LCD. It works fine with the USB but when I connect the power supply the text on the right of the screen is in blocks. I do have to turn the potentiometer when I move between power. The potentiometer is the bochum 3386. The power supply is 12v/.5A center positive. I'm in Europe.
I hope you connected the 12V supply to Vin, if not you probably fried it. The USB gives you about 4.5 volts for VCC on the arduino, the Vin gives you about 4 VDC on Vin. If adjusting the pot resolves the problem celebrate. You may have to try another display. This response is to help you get started in solving your problem, not solve it for you.
Good Luck & Have Fun!
Gil
You misunderstand the purpose of the "barrel jack" or "Vin" on the Arduino UNO (or similar).
This is to power the microcontroller itself. Nothing else with the possible exception of a couple of 20 mA LEDs.
You have connected something else. Albeit not much, but something other than the basic UNO. The on-board regulator - lacking any significant heat-sinking - simply cannot provide the extra current.
So, just power it properly. It requires a regulated (at least for the display) power supply of 5 V. So provide one. Either a common USB "phone charger" or a "buck" switchmode regulator from your 12 V supply.
Incidentally, you will find it much easier if you disconnect any connection from the potentiometer to the 5 V. You only need the wiper to pin 3 and one end to ground. This is a long-standing mistake propagated from one designer to the next by less-than competent people. Removing the 5 V connection will save you a trivial amount of current, but make contrast setting much easier.
Turns out I just needed a 120v/5A power supply, not .5A!