My power button had stopped working a number of months ago, and after opening up the phone and trying to fix the physical button, I realized it was the power and sensor cable. Then after over 3.5 years with this phone, I unfortunately dropped the phone and shattered the glass display. I ordered a new display and a new power and sensor cable and fixed both. (Also used all the steps in iPhone 4S Power and Sensor Cable Replacement and steps 28-31 of iPhone 4S Headphone Jack Cable Replacement)
The repair went very smoothly. The two repair guides were the same until step 26. After that, I had to switch back and forth and ensure that I took out all the appropriate parts in the right order. Replacing the display was a bit more involved as it required carefully removing tiny shards of glass around the power button while keeping the gasket and adhesive at the back of the button in-tact and ready to transfer to the new display.
Complete the repairs on a solid color pillow case or other soft surface so that anything that falls is clearly visible and doesn't slide/roll away. Don't have too much coffee or your hands will shake and it'll be impossible to put the phone back together with all the tiny screws and parts. Finally, be methodical and patient!