Battery powered Arduino - digitalWrite fail

CrossRoads:
5V wallwart. 1A or 2A or 4A
Switching DC Wall Power Adapter 5V / 1A - dipmicro electronics
Switching DC Wall Power Adapter 5V / 2A - dipmicro electronics
5V 4A Power Adapter OPENPEAK OP-20004

I should have said 'not connected' to mains power. This is a mobile hand held device so needs to self contained with a battery

I've only done 1 battery powered project, 1000mAH 3.7V LiPo powering 8 MHz Promini and 433 MHz Tx unit with keypad.
Wake up on keypad press, send the pressed button, go back to sleep. The battery is under the bare part of the green perfboard (Velleman ECS1/2, island of holes perfboard)

3xAA battery pack for bootloading and prototyping if a small board with not much on it, like my standalone programmer:
http://www.crossroadsfencing.com/BobuinoRev17/