Are you burning the mpeg file straight to a dvd? Or are you converting to dvd-video, then burning?
Mpeg files come in all shapes and sizes. DVD-Video has fairly stringent requirements on resolution, frame rate, and type of audio used in it. Many mpeg files that play on computers, simply don't work on stand alone dvd players without converting/authoring to dvd-video standards.
You could try converting the mpeg file or the avi file to dvd video in DVDFlick. It is free to use.