I don't have experience fixing Playstations, but regardless opening a machine as an expensive as a PS3 without using the right tools is something I wouldn't advise. If you break the casing because you improvise you'll feel a right fool, even if you later complete the repair yourself. Sometime in the future you may want to sell the PS3 to get a newer (as yet unannounced) Sony console with backward compatibility, and a cracked case would drive down the resale price far more than the price of a T10 screwdriver. If I were you, I'd pay for the ifixit YROD kit and watch the repair tutorial until I know it inside outside before attempting to repair it.
If other headphones function perfectly I don't see how it could be a contract problem with the jack, unless the headphones are visibly damaged or even bent at that end. As for isolating the fault, the simplest, most certain thing to do seems to be to replace the length of the wire. I don't think iPod earphones upon and close without a lot of visible damage, so if it is something inside the speaker the even replacing it might make the repaired earphone uncomfortable in your ear.