Yes, old gas is a common problem. It starts to go stale after just a few weeks and turns to jelly in a few months. Drain your tank and drain the carb using the drain screw on the bottom of the float bowl. Refill with fresh fuel and change the spark plug. It will either work or it won't, depending on whether the gas turned to jelly or not.
If that happened, you will need to remove the carb and clean it. This is best done in a special carb cleaner like the one sold by Yamaha. It is formulated to remove varnish from the jets and passages.
When storing the machine it's best to drain the tank and carb or at the very least use premium fuel and SeaFoam additive in the tank. I've had no storage problems when doing that with my bikes and ATV's. It's cheap insurance and saves a lot of work in the spring!
If the machine hasn't been tuned in awhile, now is a good time. It's always a good idea to change the oil in the spring to remove any moisture from winter storage.
It's also a good idea to check the valve settings at least once a year unless it doesn't get much use.