Sorry for posting this as I finally figured out one way to do this! In case anyone else has had any problems, here is what I discovered.
In order for me to paste a clip from one file to another, the destination file needed to have at least one clip already on it. So what I did was import a video into the file as if to edit it, and then I was able to paste a clip from another movie project into this file, placing the new file beside the existing video clip. I guess you have to have at least one clip holding a place for the paste function to work.