I have this iPhone 5c to repair, but before I start, I want to turn it off. When I hold down the power button, I get the...

From your description it looks like your backlight has died. I had a similar problem and you will either need to do a logic board repair by replacing a faulty chip or this may be an issue with the display its self. Try googling "macbook pro backlight" and look at some of the results.