Connection with shore power does not work?
Do you have a converter along with an inverter? Converter is bad or the 120 volt supply could be defective It is possible that the 120 volt AC circuit has a tripped breaker or there is a GFCI receptacle tripped or bad.
Genset goes through the transfer switch and works.
Sounds like there could be two problems.
The shore power cord defective
The transfer switch is not operating properly
Please check the following and report back.
connection to shore power has no effect
You do not hear transfer switch operate when connecting to shore power