If you are getting heat at the high setting, the inline fuse is good. I agree with Bradley, what you are describing is a loose connection somewhere or a faulty part, which could either be located in the generator or in the cabinet.
Bypass the generator and plug the smoking cabinet directly into a wall socket. You will need to use a desktop computer power cord (NEMA 5-15P to IEC C13) to plug into the back of the cabinet so it can be plugged into the wall socket. Monitor to see if the element get red hot, if it gets red hot don't leave it plugged in too long. If the heating element works, your are probably looking at a problem located in the generator. But loose connections are finicky, so it wouldn't hurt to take off the back panel of the cabinet, and check the wiring.
Make sure you short jumper cord is good, and has not signs of cracks. The jumper cord is the power cord that connects the cabinet to the generator. The best way to check it is to use a multi-meter and check each wire in the cord for continuity.
Open up the generator, and check all connections. Even if the wire is connected, disconnect and reconnect to ensure a secure connection.