The power switch got pushed in during use. Once I opened the case with the help of my new spudgers, I found that the switch had become unsoldered from the board - it must not have been a very good solder job in the first place.
I attempted to open the flip video without a spudger, but couldn't. Once I got my new tools, the job was simple, the problem was apparent, and the fix was easy.
The job is always easier with the right tool!