I have an unnamed tablet that has a tiny, tiny hole just below the volume buttons on the top right. After trying the resetting instructions above, I found that doing something similar worked with the tiny hole:
# Find a paperclip or similar, something that will fit into the tiny "reset" hole
# Disconnect charger, push paperclip end into "reset" hole until you feel the internal button click in, hold for 30 seconds
# Plug in charger, hold paperclip in "reset" hole for another 30 seconds
# Release paperclip, charge indicator appears.
Keep the battery above a minimum charge level to avoid this issue. It's the same "won't charge if the battery is too low" problem that affects many many other android devices.