honda generator question

Does it have a kill switch? Silly suggestion, I know. But the last time I started my generator I pulled the cord for 2 minutes before remembering to throw the switch to "on".....

You might want to pull the spark plug and hold the electrode to the engine block. Kick the starter over and see if you get spark. If you do, it's likely fuel related. If you don't, must be electrical.

don't know how cold it is but maybe frozen fuel line....
and ditto on the kill switch, been there done that too...
Also on mine the oil level has to be darn near the top.... there is a level switch on that too. it wouldn't start if it was facing the wrong way on a gradual slope...
but it's a Robin engine...

GVA, I can't believe someone else had that experience with the Robin kill switch!
In our defense I will say that the switch isn't labeled too well.

In addition to a kill switch, my small Honda generator has an air valve on the gas cap that must be turned to the "open" position before you start it.

Those screw in fuses are most likely for the output power and won't affect the engine running. Start with the basics of spark, fuel, and compression. The way to do this is to pull the spark plug and smell it for raw gas (it should be wet if you've been cranking for awhile), then hold your finger over the hole and crank the engine to feel your finger get blown off (it should puff your finger off with gusto), and then finally rig the spark plug so that the metal hex is grounded to the engine and so that the plug boot is installed on the plug but do not hold it with your hand as you can get a dandy shock. Turn the engine over and look for the thick blue spark. Usually some electrical issue causes a spark to be dead, and usually that issue is a kill switch or a low oil switch.

My old coleman passed all of these tests so I dumped the carburetor's fuel out, refilled it from the tank, and then it started right up. Seems water or nasty fuel was in the bowl. Another time the coleman's low oil sensor failed and shut the engine off despite being full of oil. You can bypass the sensor and run the engine. I dumped the coleman after that year and now have a nice little Champion.

What is "won't start"?

Do you mean the engine cranks, but won't run. In that case, I'd start looking at the fuel and ignition systems...pull the spark plug and see if it is firing, then squirt a shot of ether or WD40 into the carb. If you see the plug sparking and the engine sputters with the ether, you've got a fuel issue.

If you mean it won't crank over, I'd start looking at any type of safety/kill switches, starter solenoid, etc. If you have a multimeter, you can check for continuity across the fuse and see if it's really blown, then check the solenoid to make sure battery voltage is present and make sure it sees the voltage signal from the starter switch.

two idiot things to check (don't ask).

Screw cap thingy on gas cap (mentioned above) it is an air vent and needs to be opened.
Is the choke on or off? I have done it both ways, and it seems to work better when it is in the correct position.

Other than that check the plug.
Other than that check the fuses.

Did you shut it down normally on it's last use?

Or, did it stop/shut down on its own?

There may be a simple clue for you in this.

I have a Honda EU2000 I had to put 10w 20 synthetic oil in it to get it to start on cold days when camping. It would start with the choke on then run for a few seconds and power down. This would continue until it started a few times and the engine would warm just enough to be able to keep the oil pressure up to keep the low oil pressure switch on.

Take the plug out to make sure it has spark and is not fouled or wet.