Hello... with the generator running plug in a socket tester and see what it says... If it says open ground then the ground is not bonded to the common wire..
That means its a floating neutral. ( Well its not really a neutral on 120V)
Anyway the quickest and easy way to fix it is to make an Edison plug. Tie the ground and common ( Or neutral together and then plug that into your generator. This will bond the gen and you should be good to go.. I do this with my coleman gen when boon docking.. as my gen also has a floating neutral....
Let us know if this helps...
Read here for a better explanation...
http://www.rvdoctor.com/2012/10/my-honda-generator-will-not-power-my.html