I agree with your findings. It sounds like your laptop's headphone jack may be bad, possibly from when the headphone cable was jerked.
http://forum.notebookreview.com/asus-reviews-owners-lounges/427556-g51j-a1-owners-lounge-34.html#pos... discusses how the headphone jack works and offers some ideas on how to fix the issue.
If your laptop is still under Warranty, cost may be mimimal, but time spent without your laptop while it is repaired by ASUS may not be... Repair/replacement by a local computer shop may be a faster alternative.
G74SX-A1 - stock hardware - BIOS 202 - 2nd Monitor VISIO VF551XVT