Major doubt 1

there are four pins on the charger. 

never thought of it before. This is a 3 cell charger.

the charger wire is ok. There's no problem on this side.

 there are five wires on the battery.

We don't know whether you can charge the battery with the four pin charger in any way. There are five wires here. red, green,black white,yellow. Is it possible? Hopefully.

Turnigy 5000mAh 4S1P 14.8v 20C hardcase pack this is the official name of the battery as given in the bill.

http://scriptasylum.com/rc_speed/lipo.html In this website I ofund out how the interconnections are for the battery. This is helpful.

On the left most end, you have the real positive terminal of the battery, on the right most end you have the negative terminal. So, technically, if we can provide a 14.8V source to the leftmost such battery, then we can use the same battery charger to charge the other 3 cells.