How to get the "Your battery is broken" message to go away?

Maybe these instructions will help you to get rid of that message.

Added instructions from the link, Alt+F2, then type in gconf-editor.

Navigate to /apps/gnome-power-manager/notify/low_capacity and untick the value.

Or a single command:

gconftool --set /apps/gnome-power-manager/notify/low_capacity --type boolean false

This worked for me:

If you have a machine with Windows as a dual-boot option, you can boot to Windows and let the battery recharge here. When the battery has recharged for a while, you can boot to Ubuntu and let it do the rest.

I run this:

gconftool --set /org/mate/power-manager/notify-low-power --type boolean false
gconftool --set /org/mate/power-manager/notify-low-capacity --type boolean false