First of all, welcome to the best SeaDoo forum; a lot of information on the site and a friendly and helpful group when you have questions.
Ya, I got 3 of these so am rather familiar.
Is this a new to you or have you had it for a while?
I highly recommend getting a brake bleeder, about $20 from Harbor Freight ... unless of course you do not mind the taste of gas by sucking on the fuel line. Hook it into the input line to the fuel pump to check the path from the tank to the primary filter/water separator thru the fuel selector (check reg/reserve/off). Watch for bubbles (air in the path is a regular problem due to bad seals).
Very common to these is that the little filter at the ends of the pickups inside the fuel tank fall off due to the lines inside the tank rotting off. Note also that these filters have a check ball in them to prevent backflow and I have seen them frozen both open and closed; shaking them around should tell you if the checkball is loose and working.
Old crud in the fuel tank can stop up the works. Fuel tank can be removed thru the forward hatch for cleaning.
If you have good flow to the input side of the fuel pump, first insure the pulse line to the fuel pump is good and secure so no leaks. Insure no source of sparks or flame anywhere around. Remove the line going to the input of the carb and put it into a bottle, crank it over several turns and you should get flow.
You can take the fuel pump apart; I do not recall seeing a diaphram kit for the external fuel pump, but I have not looked.
A lot of the experts recommend replacing the old round-body carb with the SBN square body that has the fuel pump included. Just insure you get one from a single-carb installation. If you decide to go this route, check back here and I can direct you to the expert's link for jetting.
Good luck, I hope this helps a little.
Rod