This is a far out response to your problem.
1 - Did you try to increase your display intensity. If you can get into the menu, try to increase and decrease the display intensity.
http://ctflier.com/index.php?/topic/728-garmin-696-wont-turn-on/
2 - I had the same thing; shutting down / coming back up randomly, it was driving me crazy. Turns out the battery wasn't making good contact, even though the 696 was receiving power from the aircraft. Tilted the 696 forward, removed battery, re-inserted the battery and all was well.
Tunny