Another oldie. Someone made more work for themselves by rigging up more modern thermistors than that spa calls for. It would have been far simpler to install 38415 and 38416 thermistors into the heater as they would have easily plugged directly into the control box with no go between nonsense required.
Moving on...that is your thermostat where you see some discoloration on the board. Sadly those are long since discontinued, so unless you start calling dealers all over and get lucky by finding one collecting dust on a parts room shelf, you may be at a stand still here.
With the jets: I would disconnect the pump form the control box, plug in the spa so it has power best you can tell, turn the jets on and then test for AC voltage where you unplugged the pump from. Specifically where the black and white wires go. You want to see a relatively stable 115-120 volts.
But again, if your T-stat has given up the ghost it might be time to look at an entire control box retrofit, or part ways with the tub.
Fix that circulation pump with something more appropriate than a toothpick if you keep the spa.