I have an older Bradley that uses a 10amp glass fuse in the generator. Bradley may now be using an in-line fuse inside the generator. As for the in-line fuse located in the back panel of the cabinet, often it doesn't show signs that it has blown, so use a multimeter and check for continuity. Still if that in-line fuse blew, the generator would still have power.
In addition, since it was working fine the first couple of times, and now you are not getting power to the generator, plug the generator into a socket that is not part of a GFCI outlet circuit I see that you tried multiple outlets, but you need to make sure the outlet isn't a GFCI outlet. You may need to use an extension cord to locate an non-GFCI outlet. In my area the code is that outdoor, kitchen, and bathrooms must be GFCI outlets. So you may have to try an outlet in your living room. Over time GFCI outlets can become over sensitive or go bad. Also if the problem is linked to the GFCI outlets adding additional appliances on that same circuit can cause the GFCI to trip. Even if the Bradley does work when connected to a non GFCI outlet, it's worth checking the Bradley out further.
While checking the wiring check for worn out insulation, dust or debris that may be built up at the connections, dampness around the same areas and socket..