@Jviscito Do you have just a pump, or do you have a pump relay as well? A pump relay is needed in order to increase the voltage needed to activate a pump (the Rachio only puts out 24V AC, and a pump will need normal household voltage to run). Is the big white wire the common wire for the pump, or is in a zone common?
The Rachio will not be able to water if the system isn't actually receiving water from somewhere, so we need to get your pump up and running, unless you get your water from the city now perhaps? If you have a pump relay, please post a picture so we can take a closer look.