Hello Remi,
I measure 168 ma. for my entire uBITX on idle receive (low volume, no input signal, 13.8 volt source). Since I use a 7808 as a pre-regulator my 7805 is cool enough to pinch and hold, the additional heat being soaked up by the cabinet where I mounted the 7808. That keeps heat off of the Raduino and also provides a modicum of additional filtering. I also decrease the LED backlighting on my display which probably helps a bit.
Isolate the loads and check your current. There is something wrong if you measure 350 ma at under 14 volts. With the power off, unplug the Raduino, re-apply power and measure the current. If the drain is coming from the Raduino then disconnect power again and just unplug the display. Then apply power and measure again. Take your time and measure resistances until you see something amiss. Check to see if something is touching mechanically where it should not. Check under the boards. Look for a tiny wire or solder ball. Make sure that you are, indeed, in receive mode. Please let us know what you found. 73, Don
Don, ND6T