As much as that sucks, you clearly already know the fix and are working on it. Grats to you for having the skills bro. Please work safe, 2 phase electricity doesn't play around.
Yep, if your condenser unit outside just won't turn on it's always a good idea to check this capacitor. I think it was just last year that I replaced the one in my unit installed in 2015. I went through a few capacitors with the ancient system before that!
Everyone should get awnings instead of bruteforcing the heat away. The insulation in your walls works both ways: it doesn't let heat out in the winter and inside in the summer. However, the sun's radiation passes through windows without much holding it back (without awnings or external curtains) and directly heats your home from the inside. So your house is basically a greenhouse when there's nothing covering your windows.
Im sure OP knows what they are doing here but for those that don't, be careful with capacitors. Especially larger ones like these and bigger as they can hold quite a charge for some time after being unplugged. I personally watched someone shock the shit out of themselves with this exact type of AC capacitors. They were showing someone corrosion on the terminals, bridged the connection and ended up putting his arm through a wall from the jolt.
This was me on Sunday... And then also on Monday after replacing the cap and then realizing that the fan motor was janky (which might be what caused the cap to fail)
I feel so dumb sitting here thinking you were talking about the connections. Like yeah they're supposed to be round for ease of insertion. But also could tell something was off cause they usually point in parallel directions. Then I noticed the black dome they are attached to.
Please bring this to a proper site for disposal, that thing is like a flaming poison bomb at this point.