okay... not so sure it's the board. The black marks would be clear, but that is a new board and that is not very clear. I would not buy a new heater relay board (I also saw that there was power coming from it via your volt meter... black marks normally is the sign of heater relay death.)
If you have no power to the actual board... do you not have LEDs blinking on the right hand side of the main IQ board? Like the HTR ON light or the LIM OK light?
If you use the Auxiliary panel inside the hot tub, can you turn the jets on from there?