I fought a similar fight on a utility trailer I bought. I wouldn't recommend running without a plate on the trailer, so you may be in for some work.
<rant>
My biggest frustration with the whole process was that I kept getting different answer from each of the different people I talked to at the DMV. I'd get a piece of documentation they (the DMV office) told me I'd need and the next person I'd talk to would say that won't work. That was at the Harrisburg DMV office. Personally I will never step in that office again. Any state office that has a sign stating "I can only please one person each day and you're not that person," (or something to that effect) has serious problems. I understand the joke, but in that office it's not funny.
</rant>
In the end, the guy I bought the trailer from (fortunately I worked with him) was able to drum up a title. (Having the title is the easiest way to take care of the registration.) But in the process they told me there were other ways to get the trailer registered, it would just mean having to get a bill of sale and having a guy at the police station stamp an NC ID on the trailer.
In my opinion, the best thing you can do is go to one DMV office and work with one specific person until you get this taken care of. I finally took some time from work and went to a lady at the Concord DMV office. I had her show me in writing what I needed to register the trailer and from that point on, I only worked with her.
Good luck,
Jeff