There are a bunch of cd rippers out there. A quick search through available packages should give you a good list. I usually use kaudiocreator myself, part of the kde package. But nearly all of these programs use cdparanoia as the underlying ripper. I had one bad cd myself that I couldn't get to rip with any gui program, but when I used cdparanoia directly from the command line I was eventually able to rip the whole disk.
(Note, cdparanoia itself only rips to .wav format. You'll have to use another program like lame to convert the files to mp3 or other compressed audio.)
If it's a commercial disk, I'm wondering if there isn't some passive copy protection involved. The record companies have occasionally tried to put bad sectors and other physical corruptions on the disk that computer drives choke on, but that standalone cd players can still handle because they use a different error-correction system.