I looked at the schematic and the picture and it looks like you've fried the capacitor C65, it's a 4u7 10V electrolytic capacitor. It's visible in the middle diagram on page 5 in the schematic: http://www.axoloti.com/wp-content/uploads/2013/12/axoloti-core-sch-v10.pdf
Capacitors in power input circuits is a really common way for electronics to break. It's an easy fix for someone who 1) knows how to rework surface mount components 2) has access to one of those tiny capacitors. If you go with the schematics page and the device to a professional electronics/phone/PC repair shop, they'll be able to fix it. You might need to go through a few shops since not everyone is eager to doing random repairs, even if the issue is clear. If you have a local hacklab, they might even be able to help you do the fix yourself