Firstly, the CD wouldn't play in iTunes. I have two optical drives, and it wouldn't play in either. It would just skip each song until it came to the end of the disc.
When I ripped the disc, I noticed that the process was happening way too fast. I investigated the resultant files and found that they were all about 56Kb in length.
The first track obviously had a problem, as it gave a digital screech at the very start when played. I got around this by using my secret weapon--open the audio CD, drag the AIFF file onto the desktop, then trim the offending part out using QuickTime Player Pro and export as AIFF again. I was able to successfully convert the AIFF file into AAC in iTunes.
Thinking that the first track may have caused the ripping problems, I expected the other tracks to rip normally, but they didn't. Again I got the tiny files.
I thought that I could save some time by dragging the files directly to iTunes instead of via the desktop. I discovered that iTunes began ripping the AIFFs into AACs instead of merely copying the AIFFs into the library as I expected. The files ripped properly.
So there's another way to rip songs. With some of these discs, we need every method possible.