Almost assuredly this is a voltage issue with your board drawing enough current to lower the voltage to the uC ...
When you plug in the USB, you are supplying USB current in addition to Arduino PS current. The voltage goes up beyond "brown out" and things start. Removing USB lowers the voltage but not quiet enough to force the uC into brown-out.Ray
How is that possible? The power adapter supplies 2 amps. I only have the arduino, an nrf24l01 module powered through a very small 78L33 (max current: 100 mA) and an RF module that draws 4.5 mA
This is the RF module
http://www.electrodragon.com/product/2262-2272-wireless-module/