How to Power Arduino Externally ?

Your old modem power supply should be ok for external power. I consider the arduino board power splitting between the external and USB power supplies as somewhat suspect. I have an old arduino that using an external 12v power supply connected to the barrel jack produced ~8v on the board 5v pin. I had to use a 7805 regulator chip connected between the 12v and the board 5v pin to get the arduino properly externally powered.