In the modern (newer) version of marine air conditioning
units a relay to energize the raw water pump is included in the air conditioning
unit. So an external relay box is not necessary.
However, for the older marine
air conditioners there is a separate metal box with relays in it that are activated by the turning on of the air conditioner allowing ship's AC power to flow to the raw water pump. In the older units the box had the old physical solenoid type relays. I suspect the intermediate age units switch to solid state and then in the new air conditioners it was all incorporated into the air conditioner control box
actually on the air conditioner.
If you apply ship's AC power to the box and then with the air conditioner turned off and the raw water pump wires disconnected - you should observe no voltage at the raw water pump terminals.
Turning on the air conditioner should result in seeing full voltage appear at the relay terminals going to the raw water pump. If not, then the relay is defective or the control wire from the air conditioner to the relay box is not supplying power to close the relay.
If there is full voltage to the raw water pump terminals and the pump does not operate then the pump has failed. Energizing a "stuck" pump may have "burned-out" something in the pump, but with modern pumps this is rare.
However, in my experience, air conditioning raw water pumps fail all too often and at hundred of dollars each, it pisses me off to have to replace them. A lot of them are "magnetically coupled" pumps where the motor
shaft rotates a magnet that then tries to rotate the impeller in the pump. The impeller are sometimes only a plastic flat bar that "slaps" the water to the output hose. I believe this was done to limit the "clogging" of the pump with sea debris.
I have replaced and tried many different brands of AC raw water air-conditioner pumps and have found rusted shafts; scored plastic pump housings which prevent the pump magnet from rotating and broken paddles. I have even found bent motor
shafts where most probably the pump had experienced something heavy landing on it.
The diagnosing is rather simple - take the raw pump out and hook it up to an AC power source and see if it runs. Then attach some hoses and put the inlet hose in a bucket of water and energize the pump. If water flows out the "outlet" hose which you have raised to the equivalent "head" height of the air conditioner coils then the pump is fine. The problem is in the wiring
or relay box.