Replace it. Since replacing a single port can't be done that means replacing the motherboard.
Are you sure it's the port on the motherboard, and not the cable or the screen? Replacing those is much cheaper! In fact, replacing the motherboard might be so expensive (outside warranty) that it's better to replace the whole laptop.
I have a hp envy m6-ko15dx and the port which connects to the screen on my motherboard is fried what is the best way to go about with this as I can only use the hdmi port to get display...but the touchscreen is still functional even with no display.please help guys