Pikachew, you can check the year on the HIN tag on the rear Conner of the ski. A BLK tag stamped YAMAHA######## just like your car VIN. the last 2 numbers are the year. 98 would be a 1998, 01 = 2001 and so forth.
When you say "primer ball" do you mean a pump ball like those used on a outboard boat?
If so, this is likely to be most or all of the problem. Those have check valves in them that will starve the ski of fuel. They can not be used on a jet ski and have probably destroyed the fuel pumps in the carbs. I would remove that pump ball and rebuild the cabs again with genuine mykuni carb kits not after market kits.
If the carbs are correct no primer is needed. Just the chokes will do. How ever if you choose to do so the chokes can be removed from carbs and primer kit installed. Find it at SBT, or Riva Racing, or many other jet ski parts suppliers.
Unfortunately I don't have the carb set up for you but if you have a manual you should find base set up in it.
"Rodsatheart" here on this site may have a good starting point for you. He may chime in, if not try contacting him directly. If he doesn't, post back and let me know. I can txt/call him.