I used a little alcohol on a q-tip and applied just enough to the edge of the button that capillary action took some of the liquid between the button and screen surface without dripping any into the iPod itself.
Next, I cut a strip of very sticky tape (book tape) to the width of the button and about an inch long, trimmed it round at one end and stuck it to the button. Tape extending past the button (i.e. not directly over the button) was covered with paper so the tape only sticks to the button. With this long leader attached to the button, I held it in place with my thumb and ROTATED the tape (rotating the button along with it.) After a few turns, whatever dirt was holding the button in place was loosened and the button popped back out again. Now the button works perfectly.
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