I just wrote a long response but it got flagged as spam for some reason, probably because of a link to another site.
Anyway, the long and short of it is that the Kindle 4 uses metal dome switches that are attached to the back of the logic board for the various buttons. One thing to realize is that it takes a few seconds for the Kindle to process a button touch. Some users don't realize this and push the buttons multiple times out of habit, which will cause it to turn multiple pages when it finally responds.
If that's not what's happening the next thing to do is a hard reset by holding power down for 20 seconds or more. When it eventually restarts turn wifi back on, then go to settings and change the time back.
If it's still not working then either a) there's something in the button area that's causing it to stick down enough to make the Kindle think the button's being pressed again, or b) the switch has worn out. I'd first try blowing it out with compressed air, and if that didn't work soak a Q-tip in isopropyl alcohol and squeeze it out all around the switch. Let it sit for a little while, then blow it out again. Repeat several times. That should remove any gummy gunk in there.
If it's still not working you'll have to either replace the dome switch or the whole logic board. I'd replace the logic board myself because they're available dirt-cheap. Just google Kindle 4 parts to find it.
Hope that helps!