You can't just burn the file to disk, you have to "author" it. Use Adobe Encore for this.
Now the disc works on my computer and to DVD players, but not my new Panasonic DVD/VCR player. The file format is .m2v.
I guess Panasonic has some sort of piracy projection blocking the disc.
m2v is not a DVD format
After you author the project using Encore, and you look on the DVD, you will see VOB files in the special directory that is created
You need to do some more reading about the process of creating a DVD
John is correct, in his post above. Once you have the file into Encore (several ways of doing this, as of CS3 and more in CS4), you need to "author" your Project in Encore. Part of that will be Transcoding (if you have not done this in PrPro) to DVD-compliant MPEG-2 Video and either PCM/WAV, or DVD-compliant AC3 Audio.
Once done, with any needed navigational aids, like Menus, you Burn your DVD. This can be directly to disc, or to a Folder. In the case of either, you will end up with a VIDEO-TS folder (on the DVD, or in the folder on your computer) with a very specific file structure inside. The .VOB files will contain your Video elements. All are important, and the folder name, "VIDEO_TS" is important too. Once you have this disc., it should play in your set-top players, and on your computer via a software DVD player, like CyberLink PowerDVD.
Note: for the greatest possible compatibility with set-top players, use high-quality media, like Verbatim, or Taiyo Yuden. Burn at the slowest possible speed.