Instructions
Go to Microsoft's XBox 360 Support Solutions page (see link under Resources). Click on "Console Management."
Click on "Repair Your Console." You will now be required to put in your Windows Live ID and XBox 360 gamer tag to continue. If you don't have one, you will have create a new ID.
Enter your serial number first on the repair request form. Your serial number is located on the back of the console beside the barcode. Then enter your name and contact information.
Click "Submit" and Microsoft should respond to your request within days. You can check the status of the repair request by returning to the Support page.