It has the cart where the electronics are. The long thick cord that goes under the water with the robot unscrews at the cart. The on and off switch is on the electric box at the cart. When it was working the switch would light up when you pressed it on. Now no light comes on. I might just need a new electric box.
The electronics at the cart is just the power supply.. Most of the electronics is inside the Robot.
If the power switch light is not on, it could just be a fuse inside the supply... I am not sure which power supply you have, the original ones could be opened.. They had a conventional transformer and power supply circuits.. The new ones are all solid state switching power supplies and not repairable.
It can't hurt to open the power supply and see if you can see anything obvious.. A power supply runs about $200 bucks.
I am not sure why I thought you had an AGP... I must have misread your signature.
I have the same robot. I have a little background in electronics as a technician so I took the robot apart as the power supply was fine.
I found that the desicant pack inside the water tight compartment of the dolphin exploded and all of the contents dispersed themselves on to the circuit board. Ordered the IC chip that was fried and soldered it back in. It worked for three weeks and then decided to quit working properly. It would only run for about twenty seconds and shut down.