Pumps don't have any internal relays but timers do. Are you speaking of an external timer relay or perhaps the pump centrifugal switch?

If the motor is not humming when turned on, it may not be getting power. Check the breakers, especially if you have a GFCI breaker as those tend to trip in wet weather. Also, if you have experience with electrical components, then you should also know how to test if the pump is getting power.