Some dvd players can play avi files, but not all avi files are made the same. An avi file is just a container file, and the codecs used in the video can vary a lot. Your avi file may not be compatible with your player...though I cannot say that is definitely the problem.
Normally, when you burn an avi file onto a disk, you burn as simple data files.
If you want to convert the avi file to dvd-video, you can use free tools for that, including AVStoDVD, DVDFlick or FAVC. Then burn to a disk with your normal burning program or a free program called ImgBurn.
Use good media, like Verbatim, and burn at a moderate speed.