If you are saying that if it running fine off usb and you unplug the usb and then plug in the wall-wart in dc ext pwr the barrel jack.
That the program does not run ?
Let's walk throught this step by step.
Initial conditions
Everything working fine off USB.
CONDITION CHANGE
Power removed from uC as USB is unplugged.
CONDITION CHANGE
External power applied to ext pwr jack
OBSERVATIONS
uController does not seem to start running code .(nothing happens)
CONCLUSIONS
You need a Power-On Reset circuit to initiate a reset upon application of power to external pwr jack.
file:///M:/Temp/ARDUINO%20UNO/DATASHEETS/MAX698-MAX699_POWER%20ON%20RESET%20CHIP.pdf
file:///M:/Temp/ARDUINO%20UNO/DATASHEETS/lp3470%20POWER%20ON%20RESET%20CHIP.pdf
see page 3 of this:
file:///M:/Temp/ARDUINO%20UNO/DATASHEETS/AN522.pdf