On the s3 their are around 10 pins that need to be soldered to the board. If one of those has come up from the board from a jolt or drop, it could still charge but have charging issues so it most certainly could be the port needs replacing or resoldering. If you have tried a battery I would definitely try replacing the charging port. I found a company that does the s3 port repair. Here it is: [http://rockitrepairs.com/s3-charging-port-repair/|S3 Charging Charging Port Repair Link]
DIY S3 Repair Video (need equipment and skillset)
http://www.youtube.com/watch?v=E9guHq4VegI
Hope this helps!
Jon