Just going to say, I appreciate this thread and I read the whole thing.
I manage engineers, and I know a bit about electronics. I think a couple of things need to be said about those cells in the laser hair removal device.
Those are Li-Ion cells, and pretty big ones at that. To the woman who replaced the cells and it didn't work, I honestly don't know what the issue is. It's microcontroller-based, so maybe it needs a reset after the batteries have been changed or any number of things. But the cells themselves should be able to be replaced with 26650s or even 18650s. Good new panasonic 18650s still don't have as much capacity as the 26650s, but might be easier to find. All those cells are 3.3v. The difference is how many milliamp hours of charge they hold in them, which should not affect the circuit other than how long it stays charged. If they're in parallel, as everyone else pointed out, the Volts are the same, the amps are added.
Also, though, the voltage is going to differ when the cells are fully charged. This is just a byproduct of how these things work, the voltage isn't perfect, but decreases on a curve as you drain the battery. Now, that system has a method of overvoltage protection inside of it, because otherwise those cells can actually blow up (you cannot put cells like that in the checked baggage on an airplane, and you cannot ship them via airmail). It's the same kind of battery that's inside your computer, also with loads of protections on it. So, the system inside is looking for a max and min voltage to operate in.
She said that the voltage read higher on her replacement cells (sorry, I forgot and it's a few pages back on the thread) and the unit did not work properly. So, one possibility is that the overvoltage protection on the system is getting tripped somehow.
Anyways, if I were going to replace those cells, I would probably use protected cells, and try to put them in pre-drained if possible and let the machine charge them up all the way. Of course, you could run it direct off a DC source, maybe at 3v, since that would surely fall into the range that the machine wants to "see."
I hope that helps anybody else out there who is trying to save 500 bucks on a new machine. You can PM me if you wish, though I very seldom log on here and it could be a year before I respond.
--L