I wish it was easier, too. This is the kind of problem impossible to troubleshoot without the burned discs. For instance my brother burned a Blu-Ray video with Toast that wouldn't play on his player or the person' player for whom he made the disc. I had him send it to me and it played fine on my player. It's very odd, though, for the standard DVD not to play on your player or computer.
Maybe your optical drive is failing. Maybe it will work to set a burn speed other than Best. Maybe DVD-R media will work better.
Since Macs don't play Blu-Ray format discs, have you tried playing that with VLC Media Player?