I have had similar issues in two separate instances.
1) if the light on your adapter won't turn on, you have a bad magsafe and should go to Apple for a new one. This fixed my issue the first time.
2) If you have a MacBook Pro, a MacBook magsafe may run your computer, but it will not charge your computer. Also, someone else mentioned the current drain on the outlet... I agree with this sentiment: try changing outlets and see if the issue persists.
1) if the light on your adapter won't turn on, you have a bad magsafe and should go to Apple for a new one. This fixed my issue the first time.
2) If you have a MacBook Pro, a MacBook magsafe may run your computer, but it will not charge your computer. Also, someone else mentioned the current drain on the outlet... I agree with this sentiment: try changing outlets and see if the issue persists.