Yes, you've blown D4 which is a 3.3V zener diode. Putting 5V on it without a limiting resistor destroyed it and it's failed short, acting like a low value resistor. Look at page 2 of the schematic:
Axoloti Core v1.2
This has pulled pin 4 on U1 (ENABLE) low which is why there's no power. This also pulls pin 4 of U4 low that enables power using USB (according to the datasheet for this IC, it enables when pulled low.)
If you can get an SMD 3V3 zener diode and know what you're doing, it is an easy fix - the component can be handled with tweezers and a normal soldering iron. You could use a through-hole zener if you have one and bend and cut the leads short. If you want some cheap SMD zeners try eBay or Banggood:
Banggood cheap zener diodes
I reckon there's probably nothing else that's damaged.