is there a dvd player that runs data files?

Yes there is. Philips DVD players with HDMI *can* play .avi files right off a data DVD. They even have a USB port so you can plug in a flash drive or external hard drive and play your movies from there. (The drive must be formatted FAT32)

The .avi files need to be encoded using the DivX codec. Most movies downloaded from the internet these days use this format. But there are free programs like VirtualDub that let you transcode .avi files into this format.

Here's one: http://www.amazon.com/Philips-DVP5960-Player-Upscaling-direct/dp/B000G18DR0

yu can juz do this in nero through these steps.... First of all make clear that yu use version 6. If you have an older version that supports DVD (I think all the versions after 5.5.x.x) then the process is the same. Please make sure you start Nero Buring ROM and NOT the Nero SmartStart. The new complication comes up. If you see a Wizard close it (there must be a button down right which says Close Wizard or something). Open the pull-down menu and select DVD. NOTE: If there is no pull-down menu then your version does not support DVD Select DVD-Video from the list in the left side.. select the ISO tab in the menu.. file name length select max of 11=8+3 and character set=ISO9660 in label tab put a desired dvd name then click on new... At the left of your screen you see the folders of the DVD we are going to burn. Notice the VIDEO_TS folder is red. Double click to open the VIDEO_TS folder. At the right of your screen you can see your hard drive. Browse to the folder where you have your DVD files (the files that DVD Shrink created). Select all the files. I repeat: ALL the files. Now drag and drop ALL the files you selected at the step before into the VIDEO_TS folder we opened before at your left. The AUDIO_TS folder remains empty. Now click the burn n its done.. :)

No, DVD player can't run data files.
If you want to know how to burn video to DVD to play on DVD player, I think this step by step guide would help you, it will show you the detailed steps on converting video to DVD format, burning video to DVD, it's easy to understand and works pretty well for me.
http://www.reviewstown.com/how-to-burn-avi-divx-movie-to-playable-dvd.html
Hope it helps, email me if you need further help or use http://www.ask.com to search for more answers.

No.

Your problem is not the video information but the file system. Most DVD players cannot mount the file system that supports the files on a regular data DVD.

Most basic DVD authoring tools will do the conversion in one pass. Even MovieMaker can handle that. I suggest you try creating a regular DVD with some basic tool like MovieMaker or an open source tool and let it do the conversion for you.

Good Luck