i backed up the entire library to an external drive, but when I load it onto a new computer, all the information appears (songs, etc), but they won't play unless the external drive is connected to the computer? Why isn't the sound transferring?

you did nothing wrong what you have to do go back to your old computer and find where iTunes kept your music (usually in the music folder that is listed in the windows explore, if that does not work do a search for iTunes media) then plug in your external and transfer the music from your old computer to your external. depending on the amount of music and the type of USB cable you have it should be no more then a couple of hours. Once you have done that safely remove your external and plug it in to your new computer and the transfer the music from your external to your new computer. Once you do that have iTunes go and find the music. Hopefully everything will work out