Hello and welcome to just answer. I doubt that the mechanic pulled a wrong wire. Here is what probably happened: when the battery went dead the memory in the Sony was erased, and the pairing data retained in the Sony was lost. What you will need to do is to re pair the Galaxy SIII to the Sony receiver. If you do not have the owners manual for the Sony, then go to the Sony website and pull up the manual to read how to re pair the phone.
I hope this information helps, and let me know if you need further assistance with this.
I tried to pair but I keep getting the error message "UNABLE TO COMMUNICATE WITH SONY AUTOMOTIVE"
The Sony Automotive I have is MEX-BT4000P