If you see the problem, "Samples Offline" in Ableton, this means the original audio files are no longer in the location Live expected. This may be because the audio has been moved or becaase the project/song folder is in a new location or on a new computer.
In order to copy and move Ableton Live projects from computer to computer or from location to location, you need to compile all of the pertinent files into the same folder. This is done with "Collect All and Save" in the File menu.
While is it possible to fix the samples offline problem in Live (see the Live manual), it is best to pre-empt the issue by always collecting/saving files into the project folder for easier portability.