Hello again. I still have the same problem and need to resolve it now. By now I know that it has nothing to do with trying serial communications without the USB port being connected. I also know that the reason is not the 12 V DC power supply itself (i.e. it produces clean 12 V DC)
Regarding JamesC45's comment: All I/O ports are used, but I don't think that I am drawing too much current off of the 5 V pin. The 12 V power supply can provide up to 1 A, which I do not need. If there were not sufficient current available, would it not be more likely to have this situation with the USB port only?
The symptons are still the same: When I only connect the 12 V DC power supply (WITHOUT the USB port) the pin 13 LCD flashes rapidly, nothing else happens. Unfortunately, as the USB port is not connected in this case, I can not check into the sketch what is happening. When the is connected via USB or via (USB AND 12 V DC power supply), the program executes correctly.
Is there maybe a difference between the different GND pins? I would assume GND is GND and it should not matter which of the different GND pins I use?
Thank you very much for any help.