iPhone 5 totally crazed after replacing back cover

Hi everyone! :D

I've a big problem after having replaced the back cover with a new one, the iPhone screen doesn't power on or, if it does, is quite blue without any apple or other.

The motherboard I thing is ok because when I plug it to the computer and press both power and home button iTunes finds an iPhone in recovery mode and successfully restores it, even if I plug the iPhone without touching buttons, it doesn't appear on iTunes.

The strange thing is that this iPhone turns on when it wants plugged to the electricity vibrating every second. I don't know what to do, any ideas?

Thanks