I was having the exact same problem. The power button was flush with the phone bezel and it was extremely hard to power on. You would have to press the button very hard and sometimes press against a desk's edge to power it on.
My note 2 has a small screen crack just below the home button and is still under warranty. I decided to send it to Samsung for repairs asking only to fix the power button not the small less than half inch screen crack. They declined to fix it because a screen crack voids warranty. They had to phone for 3 weeks before sending it back to me. Ridiculous.
I got it back and decided to fix it myself. I didn't have any special tools but here's what I used:
1x old plastic credit card
1x plastic card (half the thickness of a regular credit card...I used my old student ID card)
1x small Philips screwdriver
1x flat head screwdriver
1x roll of 3M Magic Tape
I followed the instructions from this video:http://www.youtube.com/watch?v=UT-2zrZ_a... to take out the screws and take out the mid plate. I've never fixed a phone like this before so I watched it over and over again. I didn't have the blue plastic tool to take out the clips so I used my student ID card to make an opening and used a credit card and ran it along to the edge to pry open the clips. Used the same method to open the two clips battery is, except on one side I used the flat screwdriver just like the guy explaining in the video.
Once the plate is out, you can skip to 6:43 in the video to see where the power button ribbon is. Now when I removed just as Alex said...three pieces fell apart:
2x sliver colour round thin pieces
1x brown piece with a black thing on one side
Its because 3 pieces aren't aligned properly your power button is not working properly.
The brown pieces has to be sandwiched between the two silver pieces (make sure all three are centered) and the black thing has to be facing towards to power ribbon not the button on the mid plate. Once all three are stacked on top the power ribbon cable side I taped with small strips of 3M tape to hold it together. It took about an hour to put this section together.
Test it. Press the whole thing and you should feel the brown piece with the black pointy thing clicking...at this point your phone should power on. Next just slide the mid plate back into the phone and once you hear the clicks that means the clips are in and sealed. Watch the guy's video...he explains it very well. Put the screws back and you are done.
Sorry I only have one pic... http://i.imgur.com/XvZTJIB.jpg
You can try and replace the power button ribbon but not sure if it comes with the three small pieces. I definitely saved at least a $100 rather than going to store and getting it fixed.