Sorry, but if your iPod is non-functional to the point where iTunes cannot recognize it, there will be no way to get any tracks off of it, so you may have to repurchase the songs. You can try contacting
iTunes Store Customer Service (select the category and subcategory closest to the issue you're reporting and you'll find a button to send e-mail to them) and explaining what happened. Reportedly in some cases Apple has allowed redownloading on a one-time basis. But don't count on it.
Good luck.