You may be just under your one-year warranty? Or purchased AppleCare to extend it? EIther way, you're going to need to take your computer and MagSafe adapter into you local Apple Store or an AASP and have them diagnose the problem. No use spending money on a new adapter if it's a problem on the power supply side.
Have it diagnosed. If you're out of warranty, you'll just have to pay to get it fixed - here's hoping that your still under warranty or purchased AppleCare.