i phone 5c screen has gone black- working in background but cannot see anything

Did you already check the general troubleshooting?

If your iPhone, iPad, or iPod touch doesn't respond or won't turn on - Apple Support

I had a similar problem as well. Black lines appear on my phone out of nowhere. After a while the whole screen went black, but I could hear my phone working in the background. Well I took it in to a Verizon shop and was told that the LED lights got burned out so that might be the problem. I also do gotta add that if you try to fix this situation yourself that could void any warranty on your phone.

Hoped I helped.

I would try a soft reset (Holding the power and home button down for about 5 seconds) to see if that helps restore any picture to your phone. If that does not help see If your phone is under warranty I would suggest going to a Apple store or contacting your carrier to see if you are eligible for a replacement. If the phone has physical or water damage the warranty may be voided. Apple offers out of warranty repairs or you could get a screen repair from a third party repair place. (Apple will not ever touch your phone again and it voids everything and makes them sad.) Another option may be an insurance replacement as well if you have it through your carrier or what not. I hope this helps! (you could also try restoring the phone, but it really sounds like a screen issue.)