15v from 20pin and/or 24pin ATX Power Supply. Connecting PSU circuits in series
First off, you won't need to combine any of the power supplies OR any of the voltage rails, UNLESS you have a seriously funky charger there.  I'm willing to bet that it came with a cable that had a car charging connector on both ends, meaning it was designed to charge from a car's 12V charging port.  All three of mine have, and all of them charged just fine from 12V.  While this may not allow you to &quot;top&quot; it off, it will work just fine.
That means you'll just have to convert one of your power supplies to stand alone operation.  Personally I just buy one of those boards that you plug the 20/24 pin connector into and it does all the work.
But if you decide you want to do it yourself, here is quick list of what you'll need to do to get it working.
** You'll be using the yellow wire(s) to supply 12V to your charger.
** You'll need to connect the green wire to ground to enable the PS(maybe with a switch)
** You'll also need to supply a load to the 5V rail(red wire), as most ATX power supplies will refuse to work if they think they are not plugged in to a motherboard. I used 3 2 ohm 5W &quot;sandbar&quot; resistors in series because I had them in my junk drawer.  From what I've seen, 5-10 ohms works, just make sure that the resistors can dissipate the power safely.  I wired my resistors to the air input on the power supply.
That's it.  At this point fire it up and test your 12V output.  Then it's just a matter of wiring your coaxial connector up and plugging it in.