I had the same kind of issue, albeit slightly different as the descriptions I read here: once connecting the MagSafe connector, the led turns green, then red (normal, as charging is on-going). However, soon after, the led turns off automatically. The only temporary fix is to turn the computer off, then the charge will proceed normally. And once turned on again, as long as the charge remains at 100%, it keeps working. And (even more) surprisingly, it's when a percentage is increasing that the led turns off (e.g. going from 82% to 83%: at the moment that 83% is reached, the led turns off). I performed the SMC reset, without success. Then, I went to the Apple store in Brussels, they told me it was likely the MagSafe connector on the computer (tested parameters, namely battery are OK). It's now in reparation and the connector will be replaced.