Pool pump problem

My pool pump has been working fine, but when I turned it on today, the motor hummed for 4-5 seconds, then shut off. I thought maybe the impeller was clogged, but that was not the case. I tried again - spinning the impeller by hand as soon as I gave it power, and it ran fine. I cut the power then restarted it without hand-spinning the impeller, but the pump hummed, the impeller did not spin, then the pump shut down. Ideas welcome.