Firstly, the most likely reason for getting no output, is for one or more of your cells being either under- or over voltage. I know you say your cells were in perfect balance, but I stumbled on this post... checked everything in detail, and found that mine wasn't.
The spec for this board says:
Overload Voltage: 4.25 - 4.5V
Charging Voltage: 12.6-13V
Seeing as that you're bypassing the circuit to charge them, I would put money on the fact that your cells were over voltage, so the protection kicked in. (Or never switched off?
) Or maybe your multimeter's 4.25V is not the same as the boards'? I'm sure you can tweak the voltage ranges with a resistor. But refer to this blog icon for my thoughts on that.
Oooor... maybe resistors or mosfets are outliers in their tolerance ranges... If it's a resistor, just pop another smd resistor on top to fix that, I guess?
Or run the board at supercooled, or superheated temperatures to push those tolerances back in line!
Secondly, I disagree with the foot analogy, because the foot is much more complex than most simple electronic circuits. But mostly because you shared the model number, so anyone could look up the schematics and specs.
Unrelated. I've thought I'd broken my foot at least 4 times in recent memory. I hardly ever wear shoes. But twice I was in a situation where I could do nothing but keep running... and after a minute or 2 of severe pain, the pain subsided somewhat... and when I got to my destination an hour in the one instance, and 2 hours later in the other, it was like nothing had happened. If I was home I would've put my foot on ice and it would probably have been sore for weeks, like it had at other times. If my foot was really broken then the severe pain would've continued for longer... or would've been too severe for me to keep running. I guess.
Okay, where's my necromancer badge?