Yes, the computer is working, but if the same drive gives the same problems in a different computer, it is an indication that the LG drive is damaged, and you should ask for a RMA. If you don't have another computer available, you can ask to a friend.
Another thing you could do is a test of the drive. Using CD-DVD Speed you can verify if your drive is working correctly.
Download latest version here (free and doesn't require installation).
Insert a disc on the drive, NOT a blank one, and go to menu Run test --> Transfer rate
After the test finish, can you post the graph here?
Another thing you could do is update firmware. Often this solve many issues.