Check if it's still under warranty. If you have a Window Live id, register the console at:
http://support.xbox.com/support/en/us/nxe/LiveIDSignIn.aspx?redirectUrl=http://support.xbox.com/support/en/us/nxe/registerdevice.aspx?step=repair
It should ask for a serial and tell you if there's any warranty left. Most likely there won't be, but it's worth a shot. If there is, you can send it in and get it repaired for free.
Also, if it's out of warranty, this is from Xbox support:
"Q: How much does it cost for an out of warranty repair?
A: If you submit your out-of-warranty console for repair through the Xbox Support Web site, you will benefit from a discounted flat charge of US$99.99. However, if you choose to contact a Support Agent to create a repair on your behalf, an out-of-warranty repair for an Xbox 360 console will cost US$119.99 (plus tax). If your Xbox 360 console is out of warranty and it has been less than three years from the date that you purchased the console, your repair will be free of charge if there are three flashing red lights on the front of the console,or if an E74 error message is displayed on the screen. Microsoft may test your console for 3 Flashing Red Lights or E74 errors upon receipt at our service center. If your console has not logged a 3 Flashing Red Lights or E74 error, and you are out of the standard manufacturer’s warranty, you will be offered a standard repair at our normal out of warranty fee. If your console is out of warranty and you do not want to pay for it to be repaired, we will return your console to you unrepaired."