Good to hear that it's 'working' again. Although, the word 'working' that was used in the original post is kind of vague. The description of the problem wasn't very clear at all. Were you trying to say that if you begin with a bare unpowered arduino, and then you connect a USB cable to it, then your arduino would remain unpowered (ie. no power to it)? From the original post....nobody knows what you meant about 'working' or 'not working'......due to lack of details.
Working....
Start with 5V and USB, both connected to the Arduino.
Sketch works perfectly.
Disconnect the USB, leaving the 5V connected.
Sketch continues to work.
Leave the USB disconnected, and unplug and replug or turn off and on the 5V.
Sketch fails to run, resulting in a visual error, (Arduino is powering LEDs.)
Basically the Arduino would lose it's ability to run the Sketch, or from my opinion: Save the Sketch, if the 5V was disconnected. Plugging in the USB cable would "save" the sketch until all power is lost.