And to clarify for the OP, he could have either or both issues mentioned, bad soft start or capacitor, but my suggestion of trying it on a residential circuit assuming one is available, is a free easy test to help find the issue.
It should run no problem off a 20a resi circuit with adequate size ext cord and may, off of a 15a with a soft start.
if it does for either or both, it’s just evidence that it may be the soft start issue or generator issue, or…who knows maybe op is using an insufficient extension cord.
There are a few different factors that the OP wasn’t specific aboot that could affect the outcome.