Those TVs are well known for HDMI failure. You are far from the first to post that exact set of symptoms with those TVs.
I researched this before and have again for you. A lot of Samsung TVs are basically junk, especially their F and C series.
On your TV the HDMI circuitry is on the main board. However the buffer board can and does also frequently fail, and cause HDMI problems.
The other thing is that these plasma screens fail often producing colored vertical lines. This is a frequent problem and NO replacement screens are now available and never will be.
As is usual with Korean manufacturers parts are always hard to come by. Last time I checked the main board was out of stock everywhere and is now.
This supplier says they are only able to keep the main board for your TV in stock for 33% of the time.
Unfortunately my advice has to be to not put one red cent into that TV.
I have noted that service techs have a severe antipathy to Korean products, especially Samsung and LG. This is particularly true of household and kitchen appliances from Samsung and LG.
They all tell the same story: - lots of problems, poor design, hard to fix and above all inability to get parts.
Ron and his family who own the Appliance Depot in Inver Grove Heights, where I do my appliance business now refuses to stock the junk. Just don't get Ron started on the stuff, especially the washing machines! This family have a huge parts business and supply the bulk if the independent repair guys in that area.