My Sony "G" battery charger would not charge its DSC-H10 NP-BG1 battery so I dug into it. The result is great and the fix was simple. This will not restore your battery to new condition though it may help in a pinch.
You will need a T10 bit with a center hole and a small blade type screwdriver.
Step 1: Dissasembly
After you remove the single hollow center T10 security bit and pry off the back cover of your charger this is what you will see. Lift the pcb from the front plastic cover and flip it to the brown side.
Step 2: Adjust the Charger
Simply turn the adjuster clockwise a small amount (8ths or 16ths of turns) until the unit charges your battery.
Step 3: Assemble and Test
I will not pretend to know how this works. If your battery shows signs of damage such as bulging I suggest replacing it rather than trying this hack. Pay attention to the battery while it's charging. I'm not responsible for any damage to your property.
If this works for you or you can explain why it works I would love to hear it.