kveille,i recently bought a boat out of gulf shores ala. and they do not register boat trailers there.
first step was having thre original registration from there and a letter from the DMV in Alabama stating that they do not require that a boat trailer registerd there just call they will know what you need and can fax it to you.
You will need that to bring to LA to get regesterd/but before you do that you will need to bring it to your local state trooper (troop) building for an inspection and they give you a yellow slip to go to the dmv to have it transferred.
sounds like a lot bit if you go thruugh it step y step it is not too bad.
now your sitiuation with the VIN # may be a problem call the state trooper's they may be able to tell you.
I am sure it has to have a VIN # onn the trailer somewhere unless it is homade.

I bought a boat from my paw in law a few years ago from Ms. It was a nightmare getting the paperwork done. I don't really remember the particulars, except for the fact that I swore I would never buy another boat from out of state. It's not like a car, where you only deal with one state agency. You have to deal with DWLF and DMV. You already sound like you have issues with the deal, I would steer clear. Just my .02 BTW, if you do this, get your best tennis shoes on, because you will have to jump through many hoops.