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I would stick the drive back in the old computer (assuming the old computer still works!), fire up Address Book there, select all of the cards, and do File->Export vCard... to send a file containing all of your contacts to the desktop. Transfer that file you created to the new computer, double-click it, and all your contacts should be imported.

Was there a reason you didn't want to use the Migration Assistant to move all of your stuff over from old computer to new?