Just out of curiosity, have you tried to charge the battery directly (without the BMS and case)? Might be a long shot, but I wonder if the bms is just crap and not charging that cell. I have seen pictures of that white goo stuff on these packs before, but I am not sure that means that cell is beyond hope. If you could somehow get 3.3v of charging on that cell, it would be perfect, but if you can hit the whole pack with 26.7v or so on the main terminals and just see if the cell rises at all. It will take a while to get the other cells up to 3.65max, so you will have time to measure.
Here are some resources on taking the pack apart:
I know these are long gone for the most part, but if you happen to have some and are still looking for a solution to the terminals, here is what I did. I got this idea directly from this video, I just took it a little bit further. I started out by striping the heatsinks off the top and...
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