I have looked on various different threads that seem to have the same problem but it sounds like everyone is having slightly different issues then me because none of their solutions worked. (See below for threads I tried).
I am trying to power an Arduino Nano on external power (5.2V). When I had the Nano plugged into the USB port on the computer, it ran as expected (the Nano is powering an LCD screen) and the desired message showed up on the screen. However, when I plugged the Arduino into a 5.2 V power source from a battery, the screen lit up white and the Arduino power LED turned red, but the program written on the Arduino did not run and display on the screen.
Originally I tried plugging the 5.2 V power source into VIN, but I understand that the VIN on Arduino requires 7-12 V. (Source:voltage level - What are the 5V and VIN pins for? - Arduino Stack Exchange)
I tried switching the 5V and 3V3 on the Arduino, and power the Arduino with the 5V pin and power the LCD screen from the 3V3 pin. (Instead of powering the Arduino from Vin and the screen from 5V). Not only did that not work but it is also apparently not good to supply voltage via the 5V pin and bypass the regulator, although one website said "If you want to supply regulated power, then a 5V regulated adaptor needs to feed the 5V pin instead. (power supply - Powering Arduino Nano 12volts - Electrical Engineering Stack Exchange)
I tried connecting the TX and RX (pins 0 and 1) with a wire and also with a 10kOhm resistor but neither worked. (Program not starting with external power supply - Troubleshooting - Arduino Forum)
I do have a Serial.begin command in my code, as well as a bunch of other Serial.___ commands in my code. This thread suggests that serial commands cause problems, but does not mention what to do if that is the problem (Program not starting with external power supply - Troubleshooting - Arduino Forum).
I wanted to use the 3v3 pin but apparently when connected to external power the 3v3 pin is not working (power supply - Powering Arduino Nano 12volts - Electrical Engineering Stack Exchange). It also says that the RX and TX LEDs will flicker if digital pins 0 or 1 are 'high,' (what does that mean?) which does happen on occasion when I plug in different power sources: the RX LED will flicker and then go out.
Ultimately I am worried that my battery supply is insufficient. With the circuit I have set up, I need to power the Arduino with 3.3-5.2V. The LCD board can be supplied with 3.3V. Is this possible? I tried a setup where the Arduino was powered with the 5V pin and also output to the LCD screen with the 5V pin, but it did not result in the screen displaying the message - just the usual white screen. Any ideas on how to resolve this issue? Thanks in advance!