You should really get rid of the whole pack and don't absolutely try to charge it. These kind of batteries have very large flat metal pads soldered to a big pcb and it seems very unlikely to me that something fall off: your cells are probably both dead. You might carefully try to rip off the heat-shrink enclosing and carefully desolder the maybe-but-not-so-much alive cell. Then you will need to charge it, but again, this is a bad idea. If I had to do such a thing I'd do it outside, placing the battery in a fire-proof bag and I'd monitor it's temperature constantly. But I would not do that. That's 20$ on hobbyking or whatever and in my opinion it's not worth the risk ad all.
What are you going to power with the single cell anyway?
Addendum: with "get rid" I mean "properly dispose". LiPo batteries contain nasty chemicals and should absolutely not thrown like common garbage. Apart from the pollution that would derive from such an action you would also endanger the garbage collectors.
ok, so each battery has 4 cells in series, so you'll get 16.8V (fully charged) down to around 12.0V (flat), hence 14.8 "nominal". (Never ever discharge Li cells below ~3.0V/cell, or premature cell death is guaranteed).
they're 5000mAH capacity, and they're rated for ridiculously high discharge rates (at 5Amps, your discharge rate is 1C, not the 30-40C they're capable of), which means that you should be able to draw 5000mA (aka 5.0 Amps) for about 1 hour. so, you're OK there.
but, you almost certainly don't want to be putting all those batteries together in parallel to get "one big battery". all cells are different, especially as they age, & multiple cells in series (4 in this case) only makes this reality worse. Sure, you can short the batteries all together in parallel and they'll equalise each other out until they're all at the same voltage & no more current flowing between them, BUT:
(a) performance is influenced downwards to the 'lowest common denominator' (i.e. the weakest battery);
(b) a failure in 1 battery will bring down the whole system, and with that many in parallel, there's a huge amount of power behind the good ones to really wreak havoc on the failing/dead one, catastrophically so (as in fire, death, pesilence, etc);
(c) power loss in conductors is proportional to the current squared (P = V.I = I².R), so by concentrating current unnecessarily, you're actually wasting some power you don't need to. I'd go for a distributed approach, 1 battery per motor.
Best Answer
To first order, if the capacity is actually 2.2Ah ...
You would get nominally 3 minutes fly time at 44A = 20C.
You would get nominally 6 minutes fly time at 22A = 10C.
You would get nominally 12 minutes fly time at 11A = 5C.
Nowhere does the battery capacity exceed 100%.
A lower rate does trivially allow you more than 100% of the 20C fly time.
The actual capacity you get, and the discharge rate, are inversely linked. Not as strongly as the reciprocal, but you need to check what the capacity is at your discharge rate.
Unfortunately, the capacity is usually quoted at the 1C rate, for a 1 hour discharge. The capacity at 20C will therefore before lower than 2.2Ah. How much lower? This depends to some extent on the quality of the battery. This means that the nominal flight times above are really 'will not be exceeded' times.