In 1971 , boat manufactures weren't required to issue HIN's to their products. The number you see is very likely the hull number used for internal identification within the manufacture.
If you don't have a title you have to reapply for one, typically using the previous registration number that should be affixed to the forward portions of the boat. If you or someone else removed these numbers, then write down the "IL" number that used to be there, as there will likely be a stain or shadow left behind when the numbers where removed.
Simply put, the boat was titled and registered once and that set of paper work remains with the boat, regardless of ownership status, until it is declared destroyed. If the paper work is lost, you can re-apply for title and/or registration. You will not have success getting a new title or registration, without accepting the fact that you'll be reissued the old registration number (the IL number on the bow) and new title after proof of ownership. If you attempt to get a new title and then a registration, they will insist on receipts and other documentation of the boats' construction or a bill of sale from a manufacture or builder or a "statement of origin" from the same.
I mention this because people come into possession of boats without titles all the time. They remove the registration numbers and then try to get the boat re-titled in their name. If you try this, be prepared for the obvious questions by the authorities, who've heard it all before.
Since you bought the boat, you have a receipt, which is usually all you need, assuming the title is clear. In Illinois, the Department of Natural Resources handles the paper work for boat titles and registrations. You will need to apply for a "transfer of Ownership" at the very least, but you may also have to do a "title search" and a corrected title if any information is wrong. All of this can be done on line.
As for identification of the boat, well it appears you have what you need to know. She's a 1971 Polar Kraft and a 16' Jon boat. Yes, maybe it would be nice to know more about the manufacture and all that, but hundreds of boat builders have come and gone since 1971 in this country. You might have some luck looking up the manufacture if you had a HIN, with it's "Manufacture Prefix Code" and searched the USCG HIN data base. You also might have some luck with the manufactures name, but good luck, as the USCG site documentation storage and retrieval systems, are a joke and nearly imposable to sort through all the junk.