If the charger stays green when you screw in the batt, it probably isn't making a connection. That can be from an internal broken wire that came unsoldered or a failure in the small circuit board that interfaces with the charger and also controls the battery's discharge level (the amount of voltage that it supplies to the ecig). This is assuming you are comfortable that it is making a physical connection with the charger contacts.
I have had the same thing happen with an Ego batt and replaced it. Lights came on but no vapor. If the charger works with other
batteries and the atomizer works with other batteries, it's most likely a problem with that particular battery. There are tiny wires soldered between the center contact and the voltage regulator/control board and the battery. One break and it's toast. It's time to dump it and go shopping!
A USB passthrough is a personal choice, but is good for those times when you are sitting at the computer and have access to a USB port. If you choose the type that has a 360mah battery in a box on the cord, you can also use it as a walk around power source between charges. One of those will get you through a movie on TV without having to deal with dead batteries.
There are also direct USB passthroughs that work directly from the USB port. Personally, I'd steer clear of those, since there are varying degrees of control on the amount of power a USB port can produce. Some share milliamps between ports and some computers provide the full 500ma to each port. Still others have low power USB ports on the front for USB drives and low draw devices and full power ports on the back. If you over tax a USB port you could end up buying a new motherboard if the over current protection doesn't do its job.