Right, well two things of importance here.
Firstly: Did you get the display to work at one stage? If so, you need to recall what the connections and code were to do that. If you reconfigure it, then the first thing you must do is to get the simple "Hello World" example to operate in that new configuration, not any more complex code. You have to understand what changes need to be made in the code to match any changes in the wiring.
The second thing: In order to get any assistance here, you have to specify every detail of your project; the schematic diagram of how everything is connected, the identity (with Web links) of each part, and each example of code (posted according to the instructions) that you wish to make work.
Also you need to explain what you mean by "when the project is run on external power". You always need to provide a 5 V power supply for the Arduino. This can - up to 500 mA - be provided by the USB port. You may have been misled by certain tutorials into believing that you can power it via the "barrel jack" or "Vin" with a power source other than 5 V. This is only usable if you have no other shield or part connected to the Arduino (UNO). In general, you need a regulated 5 V supply (such as a "phone charger" with a USB socket if not connected to a computer) to power it by the USB connector or the "5V" pin and ground.