IPhone 5 won't turn on or charge?

When I charge it to an outlet and try to turn it on, the apple screen flashes on for 3 seconds and then the phone goes black. This repeats. When I try to charge it with a computer, nothing happens at all. I have charged the phone for a whole night, and this still happens. I have also tried using different cables, but so far, nothing works.

Take it to the store

Take it to the apple store, they might be able to fix the problem for you.