I did look at some of the specs for the LG players and found that it stated that they won't play on other units because the format is different! Now this sucks big time as I might or will have to search for another unit that will be compatible with what is so precious to me. I just thought that all the DVD layers had universal formats to play everything. Thank you everyone for your help and suggestions."
Your owners manual was printed in 2007. What may have been an odd format back then, may be more popular now. Either way, I don't see any other solution besides a computer. If you want your files back, you're going to have to use one. I know I sound like a broken record, but you did say your DVD's are very valuable to you. I would start off by installing VLC like one of the other posters said. Doing that will get a bunch of new codex's installed on your PC, which may allow the OS to recognize your DVD's. If so, then all you will need to do is transcode to a more suitable format. In the event VLC doesn't work, I can walk you through the process of downloading and using a live Linux distro. Its a fairly simple process.