It seems to be a hardware issue, yeah? Sorry to say, there's no way of really fixing it. Do you still have the receipt, or some kind of warranty? I'd take it in and get a replacement.
Here's another option if that is not available: Blue tooth headphones/earbuds. The port for the earbuds may be damaged, but your phone has bluetooth. If it doesn't work still, then there's some kind of software issue.