That is, I've never found this to be a firmware issue. First, software does not wear out. Second, the firmware for HDMI chips is in the HDMI chips. For reasons you can read on the web, Intel decided they would never (well not as of yet) allow HDMI firmware to be updated. It's burnt into the HDMI chips forever (for now.)

So try the usual. Unplug all the HDMI cables, then remove power from the set and wait over 10 minutes to let the chips reset. Apply power and the lone port/connection you need working and re-test.

If that fails and you are sure the cables are good and this is not another Slim PS3 issue, the board/boards are replaced to fix it.