So it is running for almost a minute?
In that time, does it make cold air? Does the compressor start?
My thinking is that if the start capacitor were bad, or if it was "locked up", you'd pop a breaker a lot faster than about a minute.
Having said that, a bad run capacitor will cause a unit to run both high amperage and inefficiently.
Both start and run capacitors can be damaged by overheating and time, as well as overheating and time.
Check to see if the compressor is starting. If it is, it would be interesting to know. If it is, it is almost certainly a bad run capacitor. And, sometimes the same cap is used for both.
If it were me and it were starting, I'd feel really good that it was the run cap and replace it. And, while I was at it, I'd replace the start cap (if it is different), too. It is about the same age and subject to the same environment.
If it wasn't starting, I probably do the same thing hoping it was the start capacitor, and replacing the run capacitor just "while I was at it" for the same reasons as above of environment and age. If that didn't work, then I'd start to worry about it being locked up and if there is anything to be done to free it. But, I sure wouldn't beat on anything, even a little, until I replaced the caps. It is likely to do more harm than good.
