When you copy a CD you rip it to a file on the hard drive, then write it from the file to a new CD-R. The original ripping probably had read errors, which were written to the copied disks. This causes clicks in the data. You can probably hear the same clicks on any CD player or DAC. Nothing wrong with the DAC.
Try using a better/different ripping drive in the future to minimize errors. Use a quality ripping software that can verify that the ripped file is accurate, like EAC, dbPoweramp, etc. Then if the ripping drive makes errors, the software will alert you. iTunes and Windows Media Center, Roxio do not care about the data quality of the rip/copy.