But you still might have screwed something else up by stopping the System Restore half-way through. When you create more problems, its harder to discern when a fix for the initial problem is found.
Also, it sounds like the battery is perfectly fine. They symptoms you describe would be caused by the charger, motherboard or BIOS. Lets start with the free option.
and download the latest BIOS update, and install it. It may take some time and unless you plan on throwing the computer in a the trash, let it finish. If you don't the computer will be made unusable.
If that doesn't work, then you can buy a new charger. If the charger is outputting the right amount of power, the bios automatically makes the computer run slower.