Wow. We can say now that it's dead allright. Puffed cells like that are toast. Too bad. Saving the bms might not be worth it,if a bms malfuntion lead to the battery death. It may have been allowing you to overdischarge it for example. I wouldn't know how to test the bms myself.
It was safe, it never burst into flames despite obvious damage. When I killed a 36v 20 ah lifepo4 with overdischarge, it also did not light my garage on fire, or even melt the tape on the battery. All it did was swell up like mad. In my case, I left a battery connected to a controller that was turned on, and went off to have west nile virus for two weeks. When the fever broke, I went to ride the bike and found the battery murdered. Presumably my bms low voltage cutoff did not work to save the battery.
THE LIPO RULES. NEVER ABOVE 4.3V NEVER BELOW 2.7V DON'T PUNCTURE
Ideal charging /discharging range for Lipo, 3.65v minimum 4.1v maximum
See battery technology section, FAQ thread at the top of the page for lipo noob info.