IPhone 6

The iPhone 6 is the first iPhone with pull tab adesive under the batteries and Apple rerouted the Touch ID cable reducing the chances of destroying the fingerprint sensor when opening the phone.

iPhone does not turn on
iPhone 6 is notorious for being the slimmest iPhone ever made (see Bendgate). This, combined with the softer aluminum alloy used, causes the phone to micro-bend in the pocket, eventually causing components such as the CPU to become dislodged on the motherboard and stop functioning.

This issue had been mitigated in iPhone 6s with a thicker, harder alloy used for the body.

The touch screen is unresponsive or not working
If the screen is completely intact but somehow the touch screen is unresponsive and/or the top bar is flickering, it the issue is very likely not the screen's digitizer but an IC on the motherboard so replacing the screen won't work. Some viable temporary solution could be applying some pressure on the IC using some paper or heating the motherboard (to try to melt the solder under the IC). A more permanent solution will require replacing the motherboard or replacing the Two Touch IC.