Time for our annual home repair SNAFU!!! HVAC this time...(FIXED! Now I'm cold!)

You need to get a meter that reads microfarads. It will have a setting that has mF or uF on it. The capacitor looks swollen which indicates failure, as does the rust. Make sure power is off with a trusted meter before touching anything. (The value of the capacitor should be on the label. Unplug leads before testing.)