Got this brand new GE70 just last month, everything was working well, until it suddenly decides to crash, and by crash, I mean the laptop suddenly shuts down, but this is only the battery, when plugged in the laptop works fine.
Batteries do fail.
Since your laptop should still be under warranty, try to rma the battery.
are you sure the battery is done at this point? when both the batter and the AC is plugged in... it states that the battery has 95% juice, and it states that (plugged in, not charging) I see other people getting similar problems, though not the same laptop, but same "problem"