Well, you could have saved yourself about $15 by purchasing the capacitor over-the-counter at a local electrical supply shop or possibly (graingers); and getting same day service. All you need are the specs, better yet, pull it and take to the counter for them to match it up.
It's absolutely safe for you to change it out yourself and don't worry about them holding a charge. Just be sure to turn off the breaker to the condensor unit before any repairs.
A sure sign that a capacitor is bad would be leakage, swelling or burnt connections.
However, more likely would be a bad contactor (contacts and/or coil) or burnt connections to the compressor.