You need to approach this one problem at a time -
First gfci issue. Replace the heater element. You can test the element correctly by measuring in the meg-ohms range any terminal to ground.
Second - You may or may not have an issue with the sensors and or board.
But I'd do the cheap thing first and replace the element. If your element sheath/insulation internally is compromised the the water inside the heater is literally electrified with 115 volts - and guess what is on either side of the element? The sensors. Regardless of insulation characteristics, those sensors are not grounded and are connected directly to cmos devices on the circuit board and this could lead to unpredictable operation.
http://spapartsnet.com/Spa-Parts-On-Sale The 4500 should work fine.