iPod was completely dead; nada, nothing, no Apple, no sad face; just as if it were in the off position. Ordered the battery from ifixit. Installed the battery per ifixit guide. Works like new.
The plastic tools were useless; broke one immediately. Used a blunt pocket-knife to pry open the case, which as the guide said, takes several tries. After opening the case, followed the guide instructions, installed the new battery, replaced the case, hooked up to iTunes, and it works.
To ifixit, it's a waste of your money to manufacture and include/or sell the plastic tools. If you're going to include them, come up with a different design that works.