Chosen Solution
After using, I closed cover—next time I opened it, it would not turn on, with or without power cord plugged in, and no (charging indicator) lights come on when it is plugged in. Battery had plenty of charge when I closed it down.
It appears from the following that the unit can be booted minus the battery being hooked up. To eliminate the battery as a potential source for the non-booting problem, I suggest you disconnect the battery and try booting the unit again. Why is the computer not charging or booting? Battery removal works.. For further information and tutorials (including removing the battery) see: Asus Chromebook C202 Repair