Chosen Solution
I changed out my 5c battery. Plugged it in. The screen stayed blank but it would beep every 5 secs. Searched online, said it was a problem with the screen attachments. I have taken the phone apart a few times trying to reattach the screen. Now the screen has power but all it shows is white squares across the middle and red and blue lines on the top and bottom.
Sounds like you have a defective screen did the ribbon cables when attached to logic board make a click sound?
