Every series S or X should still be under warranty,
if you have not opened it. I would call Microsoft and see if you can it repaired under warranty.
If you have opened it, then your kind of SOL but, if you have really good soldering skills you could fix it...
This guy on YouTube repairs consoles and he has done S and X series consoles
(16) TronicsFix - YouTube
Watch some of his videos. If your not really good at soldering, this something I would avoid doing yourself.
You can do serious damage to your console if you don't know what your doing.
BE WARNED !
The part I believe is standard HDMI port but, the videos should show you..