If it runs fine on another circuit, its not necessarily the capacitor.

Do you have anything else upstream or downstream from the GFCI? I had an issue a couple seasons ago with a corroded outlet (by the pool equipment) causing my GFCI breaker to trip. Replaced the outlet and everything was fixed (almost same as you.....pump would run for an unspecific amount of time after flicking the breaker a couple times). Also, Ive heard that you cant just flick a GFCI breaker back on. You should actually press the test button (which *completely* turns it off) and then flick it back on.

-Chris