My headphone port is not working.

I presume the display works and indicates that it's playing, and that you've check it with different headphones to make sure it's the player, not the headphones that's got the problem.

Did you start off by getting the sound coming and going, perhaps as you wiggle the heaphone jack? That would indicate it's the jack that's at fault. There's a teardown guide at

Digital MP3 Player HDMP3 (128 MB) Teardown

With care you may be able to unsolder it and fit a new one. (Look on eBay for one that seems to have the same connections.)

If that's not it then disassemble the player and examine the boards very carefully with the best magnifying glass you can find (a 5x jeweller's eye loupe would be good) and a good light and see if you can see any fractured solder joints, e.g. anything that moves slightly relative to the board as you gently flex it.