On Unreadable Optical Media

It was unclear as to the exact cause of the problem. It might have been that the original CDs were not of sufficient quality and the physical material has deteriorated. This is no one’s fault, as recent research indicates that the CD medium is not as stable as once thought. Or it might be the use of an adhesive label; it is thought the glues from the labels might damage the data with time, or if the label is off-center, an unbalanced rotation may lead to errors while reading from the spinning disc. Another cause of the problem may be that the discs are damaged. Even though CDs appear to be sturdy, they are, in fact, quite delicate and need to be handled with care: no fingertips on the surface, returned to protective cases when not in use, etc. Even the slightest scratch in a vital place may permanently cause the disc to become unusable.
 
In the two cases where we were successful, we spent a good deal of time cleaning and polishing the discs by polishing and waxing them using toothpaste, Brasso, and furniture polish, as advised by various websites, and then testing on a variety of different devices, computers, and operating systems. Once we were able to read and copy the data onto new discs, we report the results faculty of our work and research and provided tips on proper handling and storage.
 
Research suggests irretrievable data from CDs is not uncommon:

The foremost American authority on the longevity of various media, the
National Institute of Standards and Technology (NIST), still cannot give a
precise timeline for the deterioration of many of the formats we currently rely on  to store precious digital records. A recent report by NIST researcher Fred R. Byers notes that estimates vary from 20 to 200 years for popular media such as the CD and DVD, and even the low end of these estimates may be possible only under ideal environmental conditions that few historians are likely to reproduce in their homes or offices. Anecdotal evidence shows that the imperfect way most people store digital media leads to much faster losses. For example, a significant fraction of collections from the 1980s of audio CDs, one of the first digital formats to become widely available to the public, may already be unplayable. The Library of Congress, which holds roughly 150,000 audio CDs in conditions almost certainly far better than those of personal collections, estimates that between 1 and 10 percent of the discs in their collection already contain serious data errors.¹

Here are some links that may be of use:

• Conditions That Affect CDs and DVDs
• The Fragility of Digital Materials
• CD, DVD, PlayStation and Xbox Disk Repair

¹ Quoted from http://chnm.gmu.edu/digitalhistory/preserving/1.php . In context, this passage contains the following citation: Fred R. Byers, Care and Handling of CDs and DVDs: A Guide for Librarians and Archivists, (Washington, D.C.: Council on Library and Information Resources, 2003), ↪link 8.1a; Peter Svensson, “CDs and DVDs Not So Immortal After All,” Associated Press, 5 May 2004, ↪link 8.1b; Basil Manns and Chandrui J. Shahani, Longevity of CD Media, Research aAt the Library of Congress (Washington, D.C.: Library of Congress, 2003), ↪link 8.1c; Eva Orbanz, ed., Archiving the Audio-Visual Heritage: A Joint Technical Symposium (Berlin: Stiftung Deutsche Kinemathek, 1988); Diane Vogt-O'Connor, “Care of Archival Compact Discs,” Conserve O Gram, 19/19 (Washington, D.C.: National Park Service, 1996), ↪link 8.1d.