These are lithium polymer batteries, not NiCad. They do not need to be calibrated or drained down to 0, that is actually counter productive. The chemistry, charging, discharging and everything is completely different.
Each individual cell is charged separately if you look there are a boat load of leads going to the battery. This is known as balance charging. If you managed to actually run it slap dead as in no voltage at all there is zero chance of recovery. There is a difference between cut off voltage and you just screwed the pooch and ruined it voltage.
My advice would be to leave it sit for a few hours until everything is at room temp then plug it in overnight, DONT TURN IT ON AND PLAY WITH IT!
If you wake the next morning and its still dead.....Congratulations, you have calibrated your battery to ZERO and there is no chance of recovery. You will need to get a new battery.
No need to send to ASUS unless you are uncomfortable or its still under warranty. Batteries are plentiful and not at all hard to find and takes all of about 20 minutes to replace if you take a 10 minute coffee break at the mid point.
“Two things are infinite: the universe and human stupidity, I'm not sure about the former” ~ Albert Einstein