Clock, iMessage and flicker

My iPhone 5S has recently started to behave quite strangely. The clock shows something completely wrong, iMessage can't be turned on and when I activates the phone the screen flickers briefly.

I have tried to set the time manually, but it only works for a few minutes. I have restarted numerous times and I have tried with both reset and DFU Mode, but nothing works.

I'm not sure if it's a software or a hardware failure, since it has started very sudden.