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What are the conditions of the disc? Are they heavily scratched?
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Edit > Preferences > Advanced Tab > Importing TabDisable the option "Use error correction when reading Audio CDs" and check again. If problem still persists, please try to copy the audio with Windows media player and let me know the result.
That means, the problem is with either the disk or with the cd drive. If the cd have scratches on it, the problem is the drive can't read data from it correctly. If the disk is new and no scratches, you should try with a new CD drive. If you have another computer you can copy the music on that system with media player and copy it to a thumb drive and import it to iTunes.
Okay, try to create the disk image of that CD and then mount that CD image to a virtual cd drive and then try to import the songs from that virtual drive.
When they give the system back, if the problem not fixed; let me know. I will give detailed instructions or can try it with remote session.