Hey all!
I work as a Genius in an Apple Stores. Hopefully I can shed a bit of light for you on why you're MacBooks are behaving the way they are.
When the batteries in your MacBooks were new, they should have had a full charge capacity around the 4700 mAh mark. The batteries are designed to last EITHER 300 charge cycles and be able to maintain about 80% of their full charge capacity OR one year and be able to maintain about 80% of their full charge capacity, whichever occurs first.
The fact that your batteries have lasted over 300 charge cycles and are still able to maintain a full charge capacity of more than 4000 mAh is a testament to how well you charge your batteries: most batteries (including the one in my venerable old PowerBook) would be closer to 1000 mAh for that many charge cycles!
The batteries you both have contain microprocessors which relay information about the battery to the SMC. As the battery's ability to hold and maintain a charge diminish, the settings maintained by the SMC become outdated and need to be reset. Resetting the SMC gets the latest information about the battery from the battery's microprocessor, which it then uses to calculate how long it can last on a full charge among many other things.
I'm sure you're thinking, "but why does it power off then?" Well, despite the fact that both batteries are showing a very respectable full charge capacity considering their usage, and show as "GOOD" in the health field, they have been well used.
Because you have both tried SMC resets and found they haven't rectified the issue would indicate your batteries appear to be consumed. By that, I mean that their ability to release their stored charge is diminished.
Now: some maths to back up my theory. Power = current x voltage. Looking at both of your system profiler readouts, your batteries are outputting about 13000 mV (about 13 V) and 0 mA (exactly 0 A). In other words your batteries are outputting no power whatsoever. This is because the MacBook is relying on the mains however. My PowerBook outputs a similar voltage and a current of about -1200 mV (negative because its discharging rather than charging) meaning a power output of around 15 Watts. Your batteries are consumed, so assuming it is capable of discharging only a few milliamps, the total power output is still only about 1.5 Watts: something the SMC would detect as a power cut as difference between mains power and the battery is so great.
Consider the analogy of a tyre of a car even when heavily worn. The tyre, even though worn can grip the road as its made of rubber, but as soon as the engine relies on the tyre to transfer power to the road in normal conditions (assuming you're like me in England where its always raining, there is no such thing as a completely straight road and you like to drive as fast as the prescribed speed limit), it fails to accomplish anything.
Given that in all other respects your batteries should be working: latest firmware revision (0102) and are showing fully charged but not charging despite they cannot power the computer independently of the power supply.
Because your batteries are consumed, neither the limited warranty nor AppleCare will cover the cost of replacement. My advice is to book a Genius Bar appointment at your nearest Apple Store. The Genius you are seen by should run a quick diagnostic on the battery, and then do the same with a known good battery to ensure it is your battery and not your MacBook that is at issue. You should ask about a service battery (the same you would be given if you had a premature battery failure) as it is slightly less expensive than a retail boxed battery at the expense of a shorter warranty.
I know this is long, so I feel obligated to thank you if you managed to finish reading it.
Liam.
