mobile

hello,
i bought pretty beat up i9100 (it wasnt charging, i fixed it by replacing usb port in it). phone works now, but the battery acts weird, it discharges way too fast and charges way too slow, sometimes its discharging even if its connected to charger and it skips percentages. it doesnt generate too much heat. battery calibrations, apps that monitor battery usage and other crap didnt help and im running fresh and clean cm12 on it, and there is yellow triangle in boot animation (that might indicate some trouble). according to some internet tutorials i found i9100 is susceptible to short circuits and they indicate that soldering some ic on main board might fix it, but before i do something im probably going to regret i'd like to ask here how could i prove its really shorted and that the problem doesnt lie somewhere else. according to previous owner battery should be okay and phone was behaving the same even with completely new battery.
when i insert charger phone doesnt recognize its charging for about 10 secs and when i disconnect charger phone keeps showing its still charging for about a minute after disconnecting it.
many thanks for any help and/or suggestions.