I've looked around and had several friends have a look but we cannot figure this out.
I am running Ubuntu 12.10 on a Lenovo U310. The laptop charges fine when the laptop is off but it will not charge when Ubuntu is running. When I plug it in, acpi recognises that the charger is plugged in and charges for a second or two before going back to a state of discharging.
EDIT: The battery is definitely draining over time even if it is plugged in.
Here is the output for when acpi acknowledges that the charger is plugged in for a few seconds.
acpi -b -a Battery 0: Charging, 52%, charging at zero rate - will never fully charge. Adapter 0: on-line
EDIT 2: This could well be a hardware problem. I've made a fresh install of Windows 7 with correct drivers and I'm getting the same issue. I can run off of the A/C by disconnecting the battery so I know the adapter is fine.