Are you sure it's your port that is broken, have you tried different media? I thought mine was broken at first too, my first Micro-HDMI cable did nothing no matter which port of any device I plugged the HDMI into. TV's and Monitors still showed a Blackscreen with my PlayBook saying it's not connected. Sometime later I got a Micro-HDMI - HDMI Adapter to use a regular HDMI cable. At first there was a black screen and I thought it was my PlayBook port for sure, but then I made sure it was plugged in all the way and wiggled it around and it suddenly worked. That adapter is REAL touchy and the slightest movement could disconnect it. Then I got another Micro-HDMI cable, a shorter one, and that one consistently works.
TL;DR Have you tried other cables, that port can be picky, but not broken.