Welcome Ethan. Not sure if I understand what's charging and what's not.
They both went to 0...got that.
Now, your tablet will charge from the charger, correct?
When you dock the tablet...what happens? No dock charge or no tablet charge?
A similar thread is here. (from the bottom of the page)
If you haven't tried one, try a cold boot...not sure if it will help, but it's been known to fix alot of issues.
Dock tablet and unplug.
Turn off tablet.
Turn on by holding down both Power & Volume Down buttons...keep holding.
(not sure if you have Jelly Bean or ICS as an Operating System)
But you'll either see 4 symbols, or some white lettering top left...when you see either, release both buttons.
Tablet will cold boot.
Hopefully someone will be by with some more suggestions, but give that a shot in the meantime.