In some states the DMV will tell you who the previous owner was or who the ski was last registered to...OR... if you have a friend in law enforcement they can run the hull identification numbers (HIN) and tell you. Then you can look up the previous owners phone number via free internet phonebook services. Tell the previous owner that you got the "junk" ski for free and you are just trying to rebuild it for your kid, and ask them if they could write a quick bill of sale. That way they don't think that it is worth a ton of money and act like a jerk. Have the previous owner scribble or type out a bill of sale, maybe like this...
"I, ___(previous owner's name)__, do hereby sell/give my 19xx Kawasaki Jet Ski watercraft Hull Identification Number #ABC1230987, to __(your name)__ for $__($50, parts only-non running, whatever price is fair, etc)__." Then have them print and sign their name, and date it. That should work in most states.
Remember, whatever price you put on the bill of sale you will have to pay tax and/or fees on (most states). You can also get in trouble if you lie about the price, so let you conscience be your guide. If the ski doesn't run, you can usually have the bill of sale say, 'free' or 'gift', and mention on the bill of the sale that it is not running and/or parts only. Check your local laws or call an attorney for further info. There are title companies that do all this, but they charge a lot of money.
PS: Be nice to the previous owner! They do not have to do this for you, and they hold the fate of your new vehicle in their hands. Remember, he/she may initially think that it is some type of scam when you contact them about a vehicle that they haven't even thought about for many years. -Todd