Interesting topic. I was doing some experimentation on this very subject. It's very easy to circumvent the corrupted CDs, I managed it first time. They make the CD unplayable on a cumputer by putting a phony data track in (as opposed to an audio CD which has none). The computer reads this data track, can't and either spits the CD out or keeps trying to read it (as is the case with apple macs). By partially covering up the data track, the computer ignores it and goes onto the audio (which is what you want). There are a variety of materials that can be used to do this, which brings us onto the test.
Permanent markers Work fine, but as their name suggests, are permanent. This would be fine but when you cover a bit of the data track, you also cover a bit of the last audio track as well, which means you lose some of it. So it's best to use a non permanent solution.
Masking Tape, the sticky bit off post it notes Works fine and doesn't do anything permanent although there's always the risk that they will come off in your CD drive and fark it up, especially with the warm temperature in there which melts the adhesive.
Dry wipe Markers are by far the best when it comes to ensuring you get fair use of the product that you payed a rip off sum of money for. They're not permanent and don't damage the drive. Just mark a line from the outside of the CD over the slightly discoloured track (that goes about half a centimetre in from the edge) and enjoy music while you're doing whatever you normally do on a computer that doesn't use the sound card.