I have the Hampton Bay exterior lights with the control box that lets you set it for ON or a choice of "on after dusk for...2 hrs, 4 hrs... The box lights up for the selections but not the circuit test light. I placed my volt meter on the wires coming out of the box with it in the "ON" position but am not getting any reading. Is there a fuse inside the box to change, a circuit inside or any other troubleshooting I can do?

The black and white wires coming to the controller must have 120v. If they do not then its likely a tripped breaker or open circuit.

The black and white wires coming to the controller must have 120v. If they do not then its likely a tripped breaker or open circuit.

The wall outlet has 124 coming out according to my volt meter. I was wondering if there is a built in circuit breaker or fuse. Can I take the unit apart?

If its actually an outlet for a plugged unit a GFCI would be capable of tripping but that's the extent of anything built in. Check to see if you have a GFCI and then if you do push the trip button. If it makes a sharp click you have just rtipped it. No click, it was already trippped so push the reset.