American standard heritage 15 bad capacitor

We returned from a trip this week to find that one of our HVAC units was not cooling. I noticed that the outside fan was not turning on so I began to look further. I saw that the run capacitor was swollen and replaced it. Immediately the fan began working again.

The unit ran for a few hours and it still was not cooling. The fan turns on but I do not hear the compressor attempting to start.

This unit has a second capacitor - a starter capacitor. It doesn't look obviously swollen. Is it common that both capacitors go out? I ordered one today, but with the holiday tomorrow, I am looking at Saturday before I get the starter capacitor.

Just trying to think through what the alternatives might be (and crossing my fingers that it isn't the compressor).