Wow, wish I had some brilliant way to reset it, but not much I can suggest.
Just to make sure I got this right. You said the button backlights come one when you press the power button? Does the screen flicker at all?
All I can suggest is the basics. Remove any SD cards from the unit. Make sure you have adequate power. Good voltage. Check the connections. The power connector is known for poor connections.
Once the power buttons come on, try holding down the power button for 3 or 4 seconds like you are powering off. See if button lights go off. Then try powering on again.
If it doesnt work, call Humminbird ASAp and see about getting fixed. If under warranty I believe they still offer advance replacement if you need it quickly.
Good Luck,
Robert