First i would recommend copying both the folders VIDEO_TS and AUDIO_TS of the first dvd to a temporary folder on your computer's harddisk.
If that works, your files are not copy-protected in any way.
Then i would recommend using that temporary folder in Nero to make a brand new DVD-Video. Make sure the disc is finalised/closed and is written on a low speed (4 speed or something). You can set the speed like here :
If that works, pop this new freshly written dvd-video disc into one of those 3 year old dvd players and test it.
If it tests ok, try higher write speeds for your next discs.