I have problem with my iPhone 5. When i try to start my iphone, LCD wake up and then slowly down, then this repeat more times.
Please see a attachment link. Its posible is this battery ?
I've deleted your link which didn't show the problem. Could you please post some stills or a YouTube video link to illustrate your problem. Thanks in advance.
It looks like you might have a partial failure of the backlight plus whatever is causing iTunes to not recognize the iPhone. Do you live close enough to an Apple Store to take it in for a Genius Bar appointment to have a full diagnostic run?