Hi
I have had the same problem - got my Thinkpad Yoga on the 2/1/14. Windows 8.1 OS.
The initial power management option in 'Lenovo settings' when I installed the OS provided for an option to 'Automatically optimize for battery life’ - which I have just read elsewhere was supposedly removed as it had issues with Windows 8.1 (I could not agreee more) and got it resolved myself through some trial and error and retesting to prove the bug was repeatable for my own peace of mind as to the cause of the error.
The only reason I am telling you the above is because you might have got yourself where you are by doing what I did - and that reverting out is not as simple as turning off that 'Automatically optimize for battery life’ back to 'Full power'.
I assume the 'Lenovo settings' software is dynamically provided over the internet, because that 'Automatically optimize for battery life’ power menu option has now (fortunately) gone missing in the past 36 hours.
HOWEVER, as I am having numerous OS blue screen of death issues, I reloaded the OS from scratch off the recovery drive to try and stabilise the OS and experienced the exact same issue with the machine not recharging after the OS was reinstalled. My best guess is that they have progammed the same power management bug into the recovery disk.
Here is how I got it charging again...
1. Select 'Control Panel' under the Windows desktop (hold down the Windows keyboard key and press X at the same time)
2. Go to 'Power options' and select 'Balanced' if it is not already selected (mine was set to 'Power saver')
3. Shut the PC down
4. Turn the PC over and you will see a very small hole at the left front of the air vents
5. Stick a pin in this small hole and hold it down for about 20 seconds
6. Press the power-on button to restart the PC - and pray for no blue screens on restart - I had to weather a few - but hopefully it is just my PC that does it.
If you do get blue screen errors - follow the prompts - I had to restart a couple of times and then it got going again. I hope you don't have the same experience.
If your issue is the same as mine, this will have your PC charging again.
I can empathise with your frustration and I just hope this assists you.
Regards
Peter