A quick Google search shows some problems with that particular drive, made by LG for Dell. Those search results go back to 2007. Guess its not uncommon to find complaints though, rather than praise in such threads.
The drivers for optical drives are contained within the operating system and do not need to be replaced, which is why you won’t find them as separate downloads. There is a firmware available from Dell, found here: http://www.dell.com/support/drivers/us/en/04/DriverDetails?driverId=R130051 But this firmware dates from 2006, and may already be in the drive. It is such an old firmware, it probably won’t help much, if at all.
Since this is such an older model, your drive may simply be defective by this stage. New drives are dirt cheap these days, like this Samsung for $16 with free shipping: http://www.newegg.com/Product/Product.aspx?Item=N82E16827151256
But if you want to explore options with the present drive, you should first download a free burning program called ImgBurn. www.imgburn.com Opt out of any “extra” items when installing it.
ImgBurn is one of the best burning programs available. If you try to burn a dvd with it and it fails, it will generate a log which you can paste in this thread. This should tell us a bit more about what is going on. The log file can be found by clicking Help within ImgBurn.
You can also try the Microsoft Fix-It tool for optical drives. http://support.microsoft.com/mats/cd_dvd_drive_problems/en-us
It so rarely helps, I’ve just about stopped recommending it however.