If there is no signal on the input cable to the second directional coupler, what is likely the issue?

The situation described indicates that there is no signal reaching the input of the second directional coupler. This likely points to an issue upstream in the signal path. If the output cable from the first directional coupler's output port is disconnected, it would prevent any signal from reaching the second coupler at all, resulting in no signal at its input.

The functionality of directional couplers relies on properly connected cables to ensure the signal can propagate through the system. If one of the output connections is missing, it creates a break in the signal path, making it impossible for the second coupler to receive the signal.

While other options could indicate problems within the system: a disconnected cable to the house could also result in a lack of signal, a faulty input cable could block the signal, and a completely defective coupler would render it non-functional, the most direct and likely cause of missing signal at the second coupler's input is indeed due to a disconnection at the output of the first directional coupler. This clarity about signal paths and connectivity is crucial for effective troubleshooting in system installations.