Usually they bulge and if you know what it's supposed to look like, it's quite apparent that it's dead.
The cap is what's used to provide the power necessary for the initial start, so, it that doesn't happen, it's the quick and easy thing to check (I keep a set of the ones mine takes on a shelf ... 30 for a set of 2 and 10 minutes of time to replace or a small fortune for an HVAC guy to replace)
Your inside furnace fan might still run, but, on mine at least, the outside unit fan doesn't run if the cap is dead
Maximum Overdrive
It's all AC/DC [the album version is Who Made Who], but, they're pretty much all bangers with a couple originals for the movie.