I don't know what's happening, but, can you copy the files from the cd to usb stick on the pc that does recognise the data on the cd?
Was the data written to the cd on the same pc that can't read it?
Sometimes, cd/dvd drive don't always recognise data written on another machine (rare, but happens). Or, a particular brand of cd/dvd disk may be incompatible with one drive, but not another (a firmware update can sometimes fix this, but only try this if you are confidant, as a wrong update may damage the drive).
Hope this helps.