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when you plug your ipod into your computer and it shows up in itunes under devices, click on your ipod and below the picture of the ipod there will be 4 checkboxes, select the manually manage music checkbox...then your songs shouldn't be grayed out
 
I think you have to be manually managing the music on the iPod to play the tunes from it. If it's in auto-sync mode then all the music will be on the computer anyway (at least that's what iTunes assumes)
 
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