ImgBurn is not, in and of itself, capable of converting an avi file into dvd-video.
What you need is a good conversion program like FAVC or DVDFlick, both of which are free to download and use.
FAVC requires Avisynth and Net 2.0 to work. You just install them, but don’t ever have to do anything else with them. FAVC will use them automatically. There are links to both at the FAVC site. http://favcfavc.googlepages.com/
Use the HC encoder included with FAVC.
DVDFlick is here: http://www.dvdflick.net/
Once you convert the avi to dvd, burn with ImgBurn. Look through the guides at the Imgburn forum for instructions: http://forum.imgburn.com/index.php?showforum=4
Make sure to use good media, like Verbatim. Many problems in standalone players come from using poor quality disks, or burning too fast. It sounds like one of your players is just a little pickier than the other, so either use -R disks for it, or set the booktype on your +R disks if your burner is capable of doing this. If you let us know the make and model burner you have, we can tell you if it is capable of setting booktype to make a +R disk look like a DVD-Rom disk, and therefore more compatible.