Hi,
I've run into this problem with a friend who has a MacBook Air. SMC Reset does work, however, the last step - Press power to turn on computer can be left out. So here is the simple version.
1. Shutdown your Mac.
2. Connect your charger to your Mac. Make sure your charger is plugged into outlet.
3. On the left side of keyboard press and hold [shift] [control] [option] and Power button-keep holding (LED on charger may change state) Then release power button after about 2-3 secs.
4. Release the other keys. If your Mac powers up, shutdown. Do not disconnect anything! If it did not power up close the lid and leave it unattended for some time and do not use. Give it some time. Charging cycle count may take time to recalculate.
My friend's MacBook Air started it's charging cycle a couple of hours after performing this procedure. His LED went from Red to Amber and Green when charge was complete.
NOTE: If this or a NVRAM Reset does not resolve the problem then you should make an appointment with the Genius Bar. Make sure you have all of the symptoms you are experiencing and what you have tried so they can be well informed.
Hope this helps you.
Cheers!!