what did i break

LEDs white & unchanging, no high voltage. Most likely that means the 328P microcontroller is not running. Do you have +5v at pin 7 of the 328P? How about on Pin 1. If yes then the 328P is probably dead. It sounds like you shot 12v (or whatever VIN is in your case) into the 5v VCC bus. The 328P definitely does not like that. Other parts are probably okay. Probably. One thing at a time here.

The symptoms suggest the 328p isn't running, and your tests confirm it's getting reasonable power, therefore I believe it is dead. You could buy a 328p with bootloader installed on it, or you could try this:
www.electronicshub.org/burn-bootloader-on-atmega328/

I'd never heard of the GQ-4X beforel now. According to Google it will program the 328p if you have something called the AVRISP Connection Adapter. Perhaps you know what that means? I'm looking at
www.mcumall.com/comersus/store/mcumall_T...WillemsupportICs.asp
and searching within the page for Atmega328*.

If you buy one with bootloader preinstalled I don;t think you'll have to mess with the "fuse bits". If you burn the bootloader yourself the fuse bits will need to be configured and I'm not real sure how to do that when using an Arduino as your programmer (I have an Atmel AVRISP Mk.II that I use for this kind of thing, never tried it with an Arduino). In case you need it here are the fuse bit settings:
lfuse = 0xFF
hfuse = 0xDE
efuse = 0x05

As for the code, the clock code and clock-specific libraries are here:
bitbucket.org/isparkes/nixiefirmwarev1
assuming your clock has RGB LEDs, not NeoPixel LEDs. Read the page for more info about clock versions & code.
You will need the Arduino IDE from arduino.cc in order to compile and burn the program. You will also need to add a few general purpose libraries to the IDE. Look at the #includes at the beginning of the clock program to see which libs you need to get.

If you don't feel like messing with all this I'd suggest you contact Ian through the nixieclock.biz site. He can probably hook you up with a ready-to-run 328p for a decent price.

Forgot to mention: 33*C isn't unreasonably hot for the 7805. If it's too hot to touch (say, >45*C) then there might be a problem.

It does sound a lot like the controller took a hit. This stuff happens.

Unless you have a wish to try and dig yourself out of the hole (always a good learning experience), the easiest way is I'll just send you a new controller. You have no idea the number of controllers I have zapped over the years, and as far as I am concerned, everyone gets a second shot. Just get in touch and I'll ship a new one out to you.