Same thing happened to me last spring when I finally got round to commissioning the boat after months sitting in the marina yard. Honda EU22i, wouldn't fire for love nor money.
Nine times out of ten with a generator that's been sitting, it's the carburettor. Stale petrol goes almost varnish-like and gums up the jets something awful. Here's what sorted mine:
- Drain the carb completely — there's usually a small drain screw at the bottom
- Fresh fuel — sounds obvious but old ethanol-blended petrol degrades fast, especially over winter
- Carb cleaner spray through the jets if draining alone doesn't crack it
- Check the spark plug — pull it out, it should look greyish-tan, not black or fouled
- Fresh oil — some generators won't start with low or degraded oil due to the low-oil cutoff sensor
If you're storing a generator seasonally, either run it completely dry of fuel before putting it away, or use a fuel stabiliser like Sta-Bil — I've sworn by it ever since that marina incident.
Also worth checking the air filter hasn't become home to a mouse nest. Found exactly that in my cabin generator one February. Not pleasant.
What make and model are you dealing with? That might narrow it down — some generators have their own quirks. The Kipor inverter units I used before switching to a Victron/Fogstar setup had a notorious choke sensitivity issue in cold weather.
Others on here will likely have more generator-specific wisdom — what's everyone else's go-to first fix?