You should get a message explaining what is copyrighted. If its the audio, then its a simple fix, just get the audio someplace that isnt copyrighted (google "mp3 converter" and youll get loads of places to convert youtube videos to mp3s). If its the video however, then im afraid your going to have to get a bit more creative. Getting around video claims is more difficult, but often have simple solutions. Try little things like mirroring the video, thats what a lot of AMV makers do to bypass the copyright checker. Other small things include changing the contrast/color of the video. If you've done those things then im afraid your gonna have to get your video clips from a different source then where you got them and redo your AMV.
