Next time before trying to start, press and hold down the STOP/PRIME BUTTON until you hear the fuel pump click and then when the clicking slows down or stops, then push the START button. This will fill the carb bowl with gas and should start.
Honda has an anti theft device installed in the radio. If someone steals your radio it won't work for them when they power it back up until they put in the proper "radio code". That is what you are doing, you are switching off the power to the radio and when you restore or repower the radio, you need to enter the radio code into the radio and it will then work. If you can't find the radio code attached to your owners manual you can take your VIN number to any Honda dealer and they can look it up on their computer. Write it down for future reference because every time you turn that switch OFF and back ON you will need to enter that code again. Same thing if you disconnect the battery for any reason. So find the code or make a trip to the Honda dealer.
Try the primer button before trying to start. The primer button is the same as the stop button. Just push and hold down the Stop/prime and listen for the fuel pump to click and hold down until the clicking slows down, usually 15 to 20 seconds, This fills the carb. bowl. Then push the Start button. should start within 30 seconds. It is best to do this at the Gen set itself so you can hear the pump clicking.