sounds like the start capacitor could be bad. Also could be dirty contacts in motor... others have more expertise on this topic-- hope you find the solution. If the impeller will turn freely (turn off power before checking this) then it seems to be electrical. If the impeller won't move, check to make sure it is not jammed with debris, keeping the motor from starting up. Should be able to clear it from inside the pump basket if debris is the problem. Worst case, you might have to take the impeller out to clear it. Also, when you replaced the motor, if you did not get the shaft seal in properly, a small amount of water could have leaked during use, damaging the motor bearings, also causing it to seize up.

Sorry to not be more specific, but that should give you a few things to check out. Good luck!