AC compressor doesnt kick on in condo.

Hey guys. My GF lives in a condo here in NYC. It was built in 2005. She has lived here since 2013. We installed Nest thermostat right away. No issues with installation or anything. Fast foward to this past week and the other day I could have sworn I heard the Nest trying to kick on the AC. I heard maybe 5-6 clicks in a row like it was trying to start the compressor up. I looked at it said "waiting 4min" to kick on again. Didnt think much of it, but I did note it in my mind as not being totally normal. So friday night I wake up at 1 am in a pool of sweat. Go to Nest to see the temp & its 84 degrees in here. Also nest now says "Error E3 no power to unit", Great. Just what I needed! Next morning I whip out the multimeter and test every circut breaker here in the apt. (On a side note the kitchen under cabinet lights stopped working like 2wks ago). Two 20Amp circuit breakers did not have 120 V. One had 9.6V and the other like 2V. I used the multimeter in the outlet that shares the switch with the cabinet lights and sure enough it was giving out 9.6V. The one giving out 2V said AC. Off to home depot. Picked up Milwaukee insulated electrical screwdrivers and 2 new 20amp 1/2" breakers. Go down to the basement and I find another set of circuit breakers labeled "2nd floor" (which is us). Open it up and it has two 100 amp breakers listed as main apt and two 60 amps labeled "AC Comp". I kill the main power and ac compressor, run up stairs and use my multimeter to make sure there is no juice going anywhere. All clear. I switch the two 20 amps in the apt. At this point im super confident I have found the issue and I will be enjoying AC again any moment. Go back down turn the power back on and score 1 for me, kitchen cabinet lights work! Turn on AC next and nothing..... Damn there goes my pat on the back for fixing it. Last thing I could think of was to check the circuit breaker downstairs and make sure those were all puttting out 120V. Yes they are. Stumped again I now go look at the ac room in the apt in the closet. There is the furnace and ac unit stuff a light switch, another red light switch that says emergency gas shut off (for the heat in guessing) & a GFI outlet on the wall. I follow the troubleshooting steps on my iPhone with nest for E3 error. It has me move (red) Rc to Rh. Still nothing. Now it says please call for support. So I sit down with a tall glass of water and call. So they have me testing all sorts of wire combos, put the blue Y1 (if im not mistaken) into where the white W1 was and see if the AC kicks on as the heat. When i did that I got a small pop and i spark from behind the nest. Killed the breaker and now they had me remove all the wires and just twist blue green and red together. Nothing. Then just green and red. (Fan & power) ! The fan kicks on with power! I look again and the GFI outlet in the room with the furnace and ac stuff is tripped again after trying the blue wire before. So right now I am just turning the fan on and off with the circuit breaker I labeled. What is my next option? The only thing I can think of is maybe its a bad GFI outlet and thats somehow tied into the AC compressor? Maybe not since the fan and power wires work together? I asked a neighbor whos lived here the longest if he knows anything about this. He gave me the name of the business that installed these units. I am going to call tomorrow and see what they say. Also asked a friend whos next door neighbor is a contractor im sure he knows a certified hvac guy. I know this really isnt the place to ask for DIY instructions but anything else I can try that I missed? Sorry for this story being so long but im not a happy camper in the summer time and especially if the AC doesnt work!

Thanks to all that read this!

-Jordan