This is very, very normal for iPhones 4/4S.

This happens because of the way the button is designed. The button mechanism is 2 metal domes on top of one another. On top of that you have some yellow heat tape with a small black, dot on it. This little black dot is what lets you depress the domes, causing a short at the button base which causes the screen to power on/off.

What happens is this little black, dot just pops off over time. That is the only reason its not depressing.

You can replace it fairly easily. Disassemble your iPhone, take the motherboard out, remove the two screws holding the power button in place and pull it out. Then get a razor blade and slide it under a corner of that yellow heat tape with the dot on it. Then simply apple a new piece of heat tape with the dot on it. You can find it on many parts throughout HTC phones and iPhones or order it.
Here is what you need but you can find it at other sources and off of other parts...
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Please note all you need is that yellow tape with the black dot, if you do repair it dont try and replace that whole mechanism as it is soldered onto the flex cable.



Alternately you can have it repaired fairly cheaply. The store I work at charges $55 to do it but i've heard other places doing it as low as $35.

Don't waste your time taking it to the Apple store, all they will do is put the accessibility dot on your screen.

Alright thanks for helping me out. This helped me out a lot.

Settings>General>Accessibility>Assistive Touch - On..

This happened to my iPod too. This worked for me for a while.

Turn your phone off and where you plug in the lead blow into that. Then at the same time start pressing the button. This works sometimes as it may be dust or dirt in the way that just needs removing. Just try to have a dry mouth as you don't want to put much vapour into the phone. You should be able to start pressing the button again or hear the clicking, if so keep doing it.

If you're worried about getting vapour inside your phone don't try it, but it should be fine.

if you take it to the apple store they will give you a whole new phone it happened to me on my 4S