On the box on the left is it one of the relays burnt, one on the right maybe, can you take a close up photo of the damage, my money is on the box on the right, from the top control panel the cables run down to a part called a darlington switch, this is the switching unit, it will not show any sign's of burning, if your tub has a radio that will aslo cause a problem, I disabled mine.
The pumps can be tested on the tub by simple connecting them up to a power supply for a couple of seconds, the circulating pump can seize, can be repaired but a pig to seal.