This is a curious one. As i read the post I was expecting to write my standard "not all DVD blank media is compatible with all DVD players" response but that's not really the right answer here is it?
I always build a VIDEO_TS folder on a hard drive and then use Nero to burn this to a DVD as a data disk. I don't use the 'Video DVD' (or whatevere it's called) option. All they are are data disks with specific file structures after all.
As to why a certain PC failes to play the disk. What type of media did you use? DVD-R or +R or what? Double/single layer? Is the type of media compatible with the drive of the other PC. Did you finalise the disk. Not sure I've ever worried about this. Might be a hangover from my CD-R days. Can the PC read the disk outside of the DVD playing software?