The charging controller on the 13" and 15" unibody model is a ISL6258A part. Not certain about 17" but I would guess it is the same. I think I posted a data sheet link earlier in this thread. That will be your starting point. It is a 28 pin QFN package so 7 solder pads each side. It communicates with the SMC to activate charging and then uses a push-pull FET circuit driving an LC network to generate the charging voltage. There is a current sensing resistor (the green device) that feeds back the charging current information to the 6258. Check those FETs to make sure they haven't shorted and check the components around the ISL6258 to make sure none of them are badly corroded. Also, there are 1 or 2 FET that control the inrush current to the battery. Make sure those are not blown.