Hello i have the same problem.. but mine is with s6 edge. And also with broken LCD glass.. i cant afford to get a new LCD yet.
But i wonder if its the LCD. Or like you said the display flex cable.
Mine lights up sometimes after i press all the bottons a hundred times. But i get tired when it happen.
You think its the same peoblem??
Idk how to open my phone. So.. but i will want for someone to do it for me... but i wanna have idea of the problem so they wont trick me about what else is broken and charge me a lot. Hehehe
Thank you in advance.