Wonder if they will still reimburse me. They only noted "Computer will not turn on and there are no signs of power" for the repair, since I didn't take it in until the logic board died (did reboot randomly, and random colours on the screen).
17 Days later I had another repair on the new part for "Mac shuts down unexpectedly during use with battery".
Think my bill was around $600-$800 for the logic board replacement.