HDMI is no longer working on the GeForce GTX 750

So are you getting a signal out of the other ports? As an example if the DisplayPort connection is working maybe it's just easier getting a converter for it.

If you want to get the HDMI port working on the board does it look damaged in anyway? Often systems are pushed back on a desk or floor compressing the cable which in turn stresses the port connector. This might only need a new connector.

If you have a good diagram of the HDMI ports connection on the logic board have you tried just checking continuity between the external collection side and the solder joint inside of the different lines. Then when powered are you able to test the signals probing the logic boards port solder joints comparing it to a second board using a DVM and maybe an oscilloscope to visualize the signal.