I'm having the same problem with my iphone 6 after installing 9.3.2 software update. This is the second day in a row, I took my iphone 6 into the Store the assistant today was not remotely helpful. He stated that my screen needed to be replaced but he did not run any test. I insisted that he run a screen diagnostics and the results were that the screen was functioning properly no issues. I explained to the assistant that I believe it's the software that is corrupt due to, the 1st time (the day prior) I brought my iphone in the software was corrupted. He went off on a tangent and wanted me to upgrade to a new iphone.
I still have the problem and must press the power button and the home button, for the software to reboot in order for my screen to be responsive. However, once the screen locks or the iphone is idle for several minutes the problem reappear.
I'm not convinced that the assistant was looking for the root cause and ownership of the issue, he was a salesmen.