OK, most states just want a track record of boats, in some cases to intercept stolen craft, in others to have a record of ownership for boats which fall under their jurisdiction for motor licensing.
Go the the guy who you got the boat from, give him a token payment, get a signed bill of sale from him, perhaps indicating it is an un-numbered derelict boat he has had for "x" years. Copy it, fill out an application, enclose the fees, and send it to the DNR or whichever agency licenses water craft. Keep a copy for your self and carry it with you. (In Wisconsin, un-numbered boats get assigned a random serial number by the DNR computer and that is used for future titles. They suggest you stencil or get an engraved plate with the new number and affix it to the boat.)
Make your problem the agency's problem. Most likely they have a protocol to solve it.
Small boat, most often, small fee.
Keep us informed. Best wishes.
For hunters, Fall is the island towards which we swim all year long.