I've experienced this problem before. I'll willing to bet that you're trying to copy a dvd protected by the new Sony Arccos copyright scheme. Columbia/TriStar and New Line Cinema are known to implement this scheme. What is the movie? Look at the back of the dvd case near the bottom in fine print to see if the movie is protected by Sony/Columbia/TriStar.
You must use AnyDVD latest, DVD Decrypter latest, VobBlanker latest, CloneDVD latest, Nero Recode latest, etc... If you're going the AnyDVD route, make sure you run it in the background, and then run DVD Shrink 126.96.36.199. Many other combinations are also possible. I will not mention them to save time. In addition, I don't know what movie you're trying to rip. I'm sure others will suggest the combinations that worked for them as well.
It is unlikely your drive that is at fault rather the protection scheme. Although it wouldn't hurt to make sure all is well with your connections, slave, master, primary, secondary, udma mode 2, etc... Any bitsetting? What's the media code you're using? Burning and ripping at what speed? How much ram? What's your cpu? You get the point. Many other possibilities. Personally, I think it's a Sony Arccos issue.