you get incomplete songs for the reason that you haven't given LW a chance to downlaod them. so be patient depending on your connection, the hosts connection, the number of host, and the demands you might not get it right away. try also to download the file from many hosts, when you search there is a tab with "#" on it this means how many hosts have the song you are looking for. also sharing helps as you will get better search reasults and limewire wil favor you. this might also minimise the chances of people blocking you for being a freeloader.
BTW are the files you are looking for popular?