A Cyclic Redundancy Check error occurs when data in the files is corrupted. This corruption depends on the algorithm being used to check for corruption - it could be something as simple as converting the file to a huge binary number and dividing it by the size of the expected number - if there's a difference, then an error is reported.
If the file plays OK on another application, then that suggests that there is nothing wrong or corrupt with the music part of the file, but that the part of the file which tells the application how to interpret the music is not what is expected by the application.
In short it sounds like the problem is in the file header - so re-encoding the file(s) could sort this out.
If the music is already in data format, you could simply copy the data to a folder on your computer (presumably a PC rather than a Mac?), then play the music in Media Player. I've never used iTunes, as I don't see the point.
Try using a program such as WavePad (FREE!!!) to open the files and save them into the format you are using. WavePad allows batch conversion of files, so you don't have to open each in turn.
Hope some of this helps!