whatever the price to buy it new
Not true - you can get out of warranty service from Apple for things such as this (as long as it's not in multiple pieces), and it's a lot cheaper than the original price. For example, out of warranty service for a 4th gen 64gb is $199.
See here for more details
If you bring it in, you might find a nice enough Genius to replace it for free. You never know-- there have been many stories like this.