Try turning it on in a dark room and see if any picture comes through for that brief flash. You can also try a flashlight on it (the opposite of course). Something to test if a picture is coming through. It could be something as simple as the display inverter, though I never remembered hearing "clicks" when I've dealt with them in the past.

Since it does power on for a brief second, that does provide some hope. Tell us what you find out!
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