You can pull up the logic board and can push back in the power button so it snaps back into place in the outer housing.
If you snap it back into place, drop the logic board back down, and you feel a click then the button is working. However, if the button is making contact to the button switch at the end of the flex cable and still doesn't work then you'll need to have the power/volume flex cable replaced.
If the flex cable is ripped, or even if there is a problem in the button switch, you need to contact a company that specializes in iPod repairs. Replacing that ribbon/flex cable requires soldering withe the right equipment and with someone that is experienced. And I mean experienced in de-soldering, and re-soldering parts. I see tons of iPods on e-bay for sale, on the cheap, and if you ask the seller if they did any soldering on the board 99% of the time the answer is yea, and I lifted the solder pad off (very bad, and VERY VERY difficult to repair when a pad is lifted).
If you shoot for it yourself though, be sure to come back to the iFixit forums ... all the gang here will help you with any questions you may have.