This is a very complex series of events. If the car charger was damaging to the battery, it may have been damaging to the battery IC chip. You scratched into Comm Board to reexpose a battery contact trace, too. When iPhones perform as yours this is what I would do. Clean the dock port pins very carefully with isopropyll alcohol. I know this sounds like an out of place recommendation, but pin corrosion can cause the symptoms and is very easy to do. Second I would restore the iPhone firmware so that the battery, hardware and system can sync. back together. Again maybe a strange recomendation due to all the hardware changes you made, but it is simple and maybe will fix it. Third if these fail, I would open iPhone up, remove the 3 Logic Board screws, do not remove logic board (this is just to loosen it) and flip the Connector lever on the Home Flex cable open, jiggle the flex around a bit, set it perfect and then flip the connector clamp back closed. Screw Logic Board back down. Maybe this will help. Good luck. Brad