Chosen Solution
macbook pro, 15 retina A1398, suddenly stoped dead, battery was at ~50%, would not turn on, trying resetting g, no good. When plugged to power, mag safe led turns green and stays green, battery not charging. Related question: removed ssd, how do I read it on a working mac?
Sadly there is no means to remove the storage chips from your system to recover the data on them.
At this point I think the smarter direction is to visit an Apple Store to see if they can plug in a fresh battery to see if the logic board and the rest of the system is good.
