Did you create a data DVD? Standalone DVD players are designed to play movie DVD's - these have a very specific file and folder structure. If you look at them in Windows Explorer, you can see folders like VIDEO_TS, AUDIO_TS, and files like .VOB .BUP and .IFO. The format of the videos on those is MPEG-2.*
You should be able to create such DVD's if you pick make movie DVD in the menu (it might ask you to have the files already authored (meaning with the special directory structure, and already converted to MPEG-2) using a DVD authoring program like Nero Vision I think). If you pick data DVD, it will just copy the data without any conversion (no conversion to MPEG-2 nor creation of the special directory structure).
I should note that if you created a movie with Windows Movie Maker, the output should be in Windows Media format (extension .wmv). Did you mean your source (original file) was .avi?
Other notes: Some DVD players can also play VCD's (also special structure, but MPEG-1, and on CD instead of DVD) and SVCD (like VCD's, but MPEG-2), and MPEG-1 or MPEG-2 data files. Newer DVD players can play certain data CD's and DVD's with AVI files encoded in the DivX or Xvid codecs. You can find them with the label "DivX-certified".
One last thought: check the type of media supported by your standalone DVD player. Perhaps you burned a DVD+R when it can only read DVD-R, or vice versa.