Usually this is a trackpad issue, but it can be caused by the battery or logic board. Have you tried reconnecting the old battery?
With the bluetooth and camera, check the silver plug in connector to the left of the board for burnt ferrite beads (little silver and black square things, will look slightly burnt and expanded if bad) and try to reconnect it (while battery disconnected). I have had to replace a lot of these in this area, they seem to burn out very easily. Try a NVRAM and SMC reset as well, since it is strange for both to stop working.