The Battery doesn't look in anyway physically damaged. The contacts look good both on the board and the battery. It also looks the the battery connect directly to the board (No wires) and this also loose intact (but only from examining through the batter compartment).
When the machine is booted up, it says the battery is 7% but not charging. On boot up, is says the battery is not recognised. Pretty sure the Bios is up to date, and as this happened from a fall, it would be unlikely that this bios update would be at the same time.
Does this leave the battery damaged?