I don't know if I said this yet, so I will say it now... it is NEVER a good idea to try wiring it different ways without KNOWING exactly what is a valid wire out, damage can be done that way, and I assume based on the picture that you have done some research or have experience with this.
I wonder now if I was misinterpreting what you were saying. Did you simply switch the 2 yellow wires on the FC? Or did you take them off the FC and tack solder them together thereby bypassing the video circuit on the FC altogether? It is always possible that you have more than one bad part, and it is also possible that static damage, or improper wiring, has killed more than 1 part. I believe you (please test this!) if you say that the goggles have snow, then you plug in the battery, and then the goggles have a black screen, if so then the vTX is at least good on the TX side, but perhaps it has been damaged on the video receive (input) side. It isn't always easy to troubleshoot these things, sometimes there is a "test" you can do by wiring it in certain ways (like bypassing the FC altogether, or powering the vTX and/or camera directly off the battery pigtail where it hits the board on the quad IF they can take VBat voltage levels, etc) that will help narrow the field on the failures. I can't tell exactly what cam or vTX you have, but I assume the 9v/cam and 5v/vTX are appropriate based on their documentation. There is actually quite a few possible failure points in all this, and it is impossible to say what it is without some very methodical testing, and usually some extra parts to do that troubleshooting. Sorry, it is a little hard to guess at this stuff without some working baseline, right now based on what you have said I don't see any signs of any of the 3 pieces working.