Look for a bulged capacitor. Sure visual indication of failure.

I too thought it was the cap. Pulled it out and was about to go get another when I recalled the cap was only a year old. So I pulled the cap out of my other a/c unit and put it in the non working unit and it still did not start.

Then I started to trace circuits and tested each leg of the contactor to ground and saw 120v on both legs, so I thought it was fine and kept looking for another reason.

Finally it dawned on me I never tested between the two legs for 240v and sure enough no 240v. I had been seeing backfeed on one of the legs.

Turned out the issue was a burned out contact point on the contactor.

Replaced the contactor for $19 and all is fine again.