OK, by the information that you provided it appears that the problem you have is with burned DVD copies of original DVD's. There are three possible reasons for this:
1. Your drive just doesn't like burned DVD's.
This is the most unlikely
of the situations but it does happen. Sometimes a firmware update will resolve that problem and I recommend a firmware update regardless of how your proceed
. You didn't provide the model number but this appears to be the firmware update for your model as described. If not, browse LG's site for the exact one.
2. Bad/Cheap Media:
Cheap media is the most common reason for copies not being read by some DVD drives and stand-alone units. Always use higher quality media for your burns. Verbatim is probably the absolute best and most reliable. I also use Sony and TDK as well. Avoid off-brands like the plague.
3. Burning Software:
The second most common cause of burned DVD's not working. LG's I believe come with Power DVD OEM now (I know my Blu-Burner did) and they used to come with Nero. But they use to come with Nero and older versions of Nero were notorious for their burns not being compatible with certain drives (the problem was resolved in later releases) so I recommend for your burns that you use either the OEM of the software that came with your burner or a the latest version of Nero.
Now, if we're talking about DVD's of movies (which I assume that you are because you mentioned that the originals "play" and when talking about data, people don't normally use the word "play.") then that means you're using a keybreaker software to break security features and CSS keys and a separate software to burn (or you're using DVDFab which is notorious for failure rates). That's a problem because often the two different programs like that don't play nice. So here's what I recommend. Go to SlySoft and download the two greatest DVD burning products ever made, AnyDVD and CloneDVD2. They are separate products designed for each other and AnyDVD is the best keybreaker in existence and it's constantly updated and in conjunction with CLoneDVD2 it makes perfect 1:1 copies of your DVD's that will NEVER
fail (provided you use decent media) in ANY
drive. Both products have a 14 day free trial on them with no personal information required so test-drive them for yourself to find out how great they are.