If you are handy with tiny screwdrivers, you could open up the player (this probably voids your warranty) and look at the jack. Its might be possible to use some pliers to sort of bend it back into shape, and then use TEENY bits of solder to reconnect any broken connections.
If the player is still under warranty, see if you can get it replaced.
Saddly, most electronic equipment made these days is 'prefab' and not intended to be repaired. Even if you send a unit to a company for warranty repair, they usually just replace the whole thing, instead of bothering to fix the broken one. Fixing can sometimes cost quite a bit more than manufacturing a new one!
So anyway.. If its not under warranty, I'd say open it up and take a look with a screwdriver and a pair of tiny pliers. If you can't fix it, you won't be in any worse situation than when you started.
Another option, i just thought of, is to start using the line-out with a headphone amp. This is, of course, assuming you have a line-out. If it DOES have a lineout, then just forget about the headphone out, and get/buy/build a headphone amp, and use it out of the line-out. If you are super-cheep, you could get a 'Boosteroo' amp for like 20$, but a more audio-friendly solution would be to build a cmoy amp, or ask JMT about his amp building services. Headroom has some nice low cost portable amps as well. Also, Meier Audio makes a nice portable amp.
Anyway, good luck with that! I had an old sony PCDP (i don't even remember the model anymore) that stopped recognizing when the lid was closed. So i used a drip of solder to bridge the tiny switch that tells it if its open or closed
Then the lid broke off a while later. And then the battery compartment. And then one of the little ball-bearing thingys that holds the cd onto the spindle. I was still using it happily, though not very portably after the lid broke off. I finally retired it after the LCD screen got crushed in. It still worked, you just couldn't see what track you were on. I suppose its a testament to the things design, takes a lickin' and keeps on tickin'
Hopefully your cd player will have as good of a record
peace,
phidauex