Transferring music cutting off the ends of songs from my old library? How can I restore these?

So upon getting my Macbook, transferring and syncing my iTunes libraries, I found that numerous amounts of songs transferred to my Macbook had the ends of songs, thus leaving the remainder of the song duration with silence. Whether I play those certain songs off of iTunes on the notebook or on the iTouch, the last minutes are missing. How can I restore these? They aren't stored in online with previous purchases or on CD's because they came off a network/family sharing. Any solutions?