I am wondering why my Arduino program won't start its sketch to connect a bluesmirf to an android device and send data to the android whenever I use an external power supply. The sketch starts whenever i open the serial monitor, but using the power supply, it wont work.
You'll probably find that you are not supplying enough power to operate the Arduino and the components attached to the Arduino. Your current (Amps) draw is most likely higher than your external power supply can output.
I had this problem when using a 9v battery to power an Arduino with an XBee chip and some LEDs attached. The 9v would be able to power the kit for a while but would then not output enough current to power the Arduino. In the end I had to scrap a few LEDs.
You need to find out how much current your Arduino and its components are using and use a suitable power supply that can output enough current to power your Arduino.
Also remember when you send and receive a packet out of a Bluetooth radio - more current is required than when the Bluetooth radio is idle.