Man I totally feel your pain! My brother gave me a boat that one of my cousins had sitting in his yard for years that he had taken in payment for a debt. He never used it so my brother asked him if he could bring it from my cousins place in ND to my place in MT so I could use it. There was no chain of ownership etc. and it came from ND where they don't title boats and trailers. It took me months to get everything I needed to get the stupid thing registered in Montana. To include having my brother register the boat in ND and get a ND boat tag for it from their equivalent of FWP so then I could get a bill of sale from him with a copy of that tag documentation showing he owned it and was transferring ownership to me. It ended up costing us several hundred bucks in the end for a "free" boat. I didn't even have the trailer issue you are having but because my trailer is a homemade job for that little boat it has no identifying numbers on it e.g. no serial number or VIN or anything like that. Eventually after jumping through a ton of hoops DMV just told me not to register the trailer because it is so small and cheap. The whole process was so incredibly frustrating I wanted to spit nails the entire time. I wish you the very best of luck, and I hope this goes easier for you than it did for me.
A lot of it is about catching stolen boats and trailers... At least in the states I deal with. Good luck!