Are you using the Nokia charger? I know that using a third-party cable doesn't always work.
Try using an official cable, else it looks like a hardware failure.
If it's in warranty period, try taking it to your local Nokia/MS Care Point.
I had the same issue last week with my 928. I tried to place it on the charger after it randomly shut down with full battery, just to see if it was minor. No charge. No screen flicker from holding power button. Nothing. Thought it was dead.
An hour or so later I come back to see its still not charging. I did a soft reset (hold power and vol down till it vibrated) and viola! It worked. Give it a try.