I'd say it's more likely a problem with the interfacing components than the ports themselves. it would be worth a shot reflowing the solder joints in the area, and testing like D54 and D57 with a multimeter, but I'd bet the problem is probably in the P13HDMI chip, that switches between the ports. Possibly Q36 since the board markings imply it's a simple bipolar junction transistor (the B, C, and E markings).
I haven't found the appropriate datasheet for that particular version of the P13HDMI, being a 64 pin package. it would be interesting to explore the possibility of removing and just bypassing that chip, but would be easier to just replace it assuming a replacement could be sourced.