Well, you probably realise you should not be operating an Arduino (UNO/ Nano/ Pro Mini/ Leonardo/ Pro Micro) from the "Vin"/ "Raw" or "barrel jack" for any project requiring parts additional to the Arduino, such as a display, but there really should be no difference between UNO and Nano.
If it is the same display you are using, then it is not particularly likely to be faulty and while as 6v6gt says, there
have been reports of dud ICs, few of us have
actually had any problems with these parts.
While you
presumably know what you are doing, I do have to suggest you give us some photos of how you are setting this up and what code you are using. The
forum instructions tell you
how to post code and photographs
must be brightly lit (such as outside daylight) and perfectly focused.
Perhaps more practically, you need to add diagnostic print statements to the serial monitor to determine whether your code is baulking or the display itself.