I see. However, the DVD-writer itself can recognize and play the copy. If the media was faulty, wouldn't it be faulty everywhere?
not necessarily, your DVD on your computer has better error correction capabilities than what is generally in stand alone DVD players. stand alone players can be quite picky about burned media.
Also, I've noticed that every single copy made by another computer is never playable by anything other than itself? (This is the problem I am now experiencing on my formerly stable system.)
that sounds like a media issue\bad burns.
Could this be a firmware problem? But I didn't update or change the firmware. The facgtory version of the firmware have always worked for me until now.
it might be. one of the reasons new firmwares are released is not only to handle new media but to handle any changes in existing media. some media manufaturer's change their dye formulations so new burning strategies are incorporated into firmware updates to handle the changes. I would definitely update the firmware.