I was on the phone with tech support for hours with this one.
I had made a movie with my iPhone, then transferred it into my iPad, but it would not sync with iMovie, even following the directions directly from iMovie app. "no projects available to copy from itunes" <--sound familiar?
Here is what worked:
Open Tunes, drag and drop your movie into your iTunes LIBRARY from your Pictures file or wherever it resides on your computer.
Then in iTunes, in your Movies Library select your movie, then under FILE, choose Create New Version>Create new iPad version. Let that complete, then drag and drop into your ipad.
You will find your movie in the photos section of iMovies.
Have fun making movies.