I doubt resoldering the battery would do anything. That is signs of a bad battery that is leaking the chemicals in the battery. Seen it a few times. That may be why you Nexus is not turning on. Try a new battery, if this does not fix the issue then some chemicals may have gotten onto the board and may have possibly ruined it. Also another though is if you are using too high of a power source to charge the battery it may have cause the circuitry to become fried and thus fry the battery as well. Replacing the battery should solve this issue however there are other things that could have happened like i explained. Good luck, i hope it just needs a battery, it should however you never know with electronics now a days.