Your MP4 may have some features to it that make it difficult to edit. (Variable frame rate, for instance.) Video on the internet often uses compression methods that make for small files -- files that are designed to be viewed but not edited.
Open the video in the free download Media Info. Set Media Info's View menu to Tree and then copy the data it displays and paste it to this forum.
Once we see what this video file is made up of, we may better be able to advise you how to proceed.