Check IR value to earth and between the run and start windings (if possible). Check the run and start winding for continuity. The start winding usualy has the higher resistance. Check the pump rotates freely by hand and that the bearings are not partialy siezed, also check the impeller and volute are not clogged with debris. A faulty capacitor will cause a starting problem, try charging it up by putting your megger across the terminals then shorting them out, your looking for a nice fat healthy spark but this is not a true test of the capacitors condition and more of a go/no-go test. Most submersible pumps depend on the surrounding water to cool them so dont run it for long periods out of water. Dont run it at all out of water if the seal chamber is not oil filled or you will damage the mechanical seal. The seal requires the water to lubricate and cool it. Being 1ph the pump may have a centrifugal switch in the start winding circuit that opens as the pump gets up to speed. If its faulty it will also cause starting problems but to determine this and check its operation the pump will have to be dismantled.