With the breaker to the condenser off, not just the stat in the off position but the breaker off, remove the black wire coming from the relay to the contactor from the contactor, remove the red wire which is coming from the exploded start cap to the other capacitor and then the yellow
bright wire which is coming from the relay to the silver dual run capacitor. remove that wire at the silver capacitor. No need to remove any wires from the exploded cap or the relay, only remove them from the contactor and the other cap.
Now the hard start kit is entreily removed from circuit. Make sure those loose wires are tied up/electrical taped and not touching anything at all whatsoever, flip the breaker to the condenser on and turn the stat to cool. If it comes on than you're good. Probably best to go ahead and purchase a new hard start kit and install it, though.