So I was tinkering and, like an idiot, accidentally shorted 5V and Vin (I had a 12V source connected through the barrel plug. Was trying to use the 12V to power a high powered LED which was controlled by a transistor connected to a relay. But I accidentally put the wrong wire into Vin...
Does anyone know which components might have been killed by this? I'm comfortable soldering in new components, I just don't know which ones to start with. I assume I need to replace the ATMEGA and the 5V regulator (and maybe other things).
If you are "lucky" only the removable atmega328p is dead. Lucky because after you removed the 328, you could use the remaining board as a USB/serial interface to program a mini-pro.
If you are "unlucky" the USB-Atmega 16U2 is (also) defective and it will be very difficult to repair the UNO, that small processor is programmed as a UART and hard to get.
It is unlikely that the voltage regulator or any other component got damaged by the 12 volt on the 5V rail.
Well I would suggest performing the following tests.
Remove the 328P chip from it's socket
Plug the Uno into the PC usb port and see if it acknowledges the connection and that it's serial port shows up in the IDE. If it doesn't you really should just get a new board.
If it does see the connection and serial port then run the loop back test (there is a sticky somewhere on this forum) and that will tell you if the USB serial chip is functioning or not. If not get a new board.
If it functions the loop back test, unplug the board from the PC and attempt to power the board with an external DC voltage (7-12vdc) to either the external power connector or the Vin pin. If you don't see a good +5vdc on the 5V pin then you can attempt to replace the regulator.
If the 5 volts is good you can put the 328P chip back in it's socket and see if you can download a sketch. If not then buy a replacement 328p chip with bootloader for $5-6.