Solution Found!
I've had the same problem of scratching off the code on the back of the App store gift cards. Found a video on Youtube with easy instructions:
1. Enter as much of the code as you can on the redeem page, as per usual.
2. Continue to enter the code over and over, and eventually a "Get Help" line will appear in red.
3. Click on the Help option, and the next screen will allow you to enter the serial number on the card. Add your email address, and Apple will send you a new code.
4. Start buying Apps!
Hope that helps.