If there is no outlet there, then you have an automatic transfer switch, maybe mounted onto the back of the main electric box with the breakers and 12V fuses. This is a gizmo that selects between the generator (when it is producing power, after a delay of maybe 30 seconds) and the shore power cord (at other times). It's possible that the transfer switch is malfunctioning.
However, before checking that, verify that the output circuit breaker on the generator itself is not tripped by flipping it off and then on. It is, of course, also possible that there's a wiring problem between the generator and the transfer switch.