Arduino nano digital pins not working with external power source
I think you may need to back up and start over again.

Rather than changing the power supply, you need to fix the problem that made you think you needed to change power supplies.

Following a link in a comment on the question you linked  to leads to this thread on the Arduino forums.

The suggestion there is that a particular pin on the FTDI chip on the Nano isn't connected as it should be.

To be exact, the Test pin (pin 26 on the FT232RL chip) needs to be grounded to fix the original problem you were having with communications with the Nano.

The description there fits your description.  The Nano can't talk to the PC if the Nano is connected to the PC at power on.  The same thing happens with the circuit referenced in that Arduino forum thread, but they are using another embedded system instead of a PC.

If you fix that, then you won't need to use an external 5V supply.

To back up the conclusion from the Arduino forum, here's an excerpt from page 8 (pin descriptions) of the FT232RL datasheet:


  26 TEST   Input  Puts the device into IC test mode. Must be tied to GND
  for normal operation, otherwise the device will appear to fail


You need to connect pins 25 (ground) and pin 26 (Test.)

Excerpt from the Nano schematic:
 

Pins 25 (ground) and 26 (Test) are right next to one another, so easy to fix.

You need to put a blob of solder on the red marked spot in this picture: