the button that fails is part of the flex.

you can save yourself trouble by just overlaying the new flex and plugging it into the board without installing it. connect battery and see if manually pushing the little actuator on the flex will start the phone. If not, you have a board problem and not a flex/button problem.

in the iPhone 5 there is a common problem of pry damage at battery replacement on the edge of the board near the SIM tray. This can dislodge components that control the lines of the home and power button. I've never seen this present as just a power button failure, but it is possible. it is also possible to damage the power flex connector on the board.

all of these are repairable, but first you need to differentiate a flex problem from a board problem.

jessa