SOLVED
I finally found solution..
http://arduino.cc/forum/index.php/topic,15257.0.html

Hi all!!!

Problems whit  external power nano need physical restart on board, before schets running. USB to computer, no problems...

Because the RX pin is unconnected, the bootloader on the board may be seeing garbage data coming in, meaning that it never times out and starts your sketch. Try tying the RX pin to ground with a 10K resistor (or connecting RX directly to the TX pin).
Tested, not help..

Any idea!!
Thanks for your time.

I have exactly the same problem. Any help...