This is two-cycle motorcycle territory.
Classically, the jets on the carb can wax up, but they are easily cleared.
I don't know the motor, but you should be able to get the jets out of the carb fairly easily and clear them, if they are gummed.
Chech for spark first. Take out each plug in turn, and lay it against the cylinder head. Turn the motor to check. You should see it easily. If one does not spark, swop the plugs to see if the problem follows the plug. If it does, then new plug is needed.
If you have spark on both pots, then you are in a strong position. If you have a wee compression meter.... the rubber-ended ones are about $20.... push it into the plug hole and check compression. Spray a wee bit of WD40 in there to give you a wee seal and some lube. My olde 500 cc Suzuki has about 150 psi on the meter, kickstarting.
If you don't have a compression meter, your thumb end will do as a coarse check. They should be about the same. If there is a hole in the piston, it will scream at you... no compression worth talking about.
If it won't start with the spark, pour a wee dribble of
fuel into the pot, turn it over once with the plug out (it must not lock up with the plug in), then put the plug in. See if it starts now. If it starts for a wee moment, then dies, then I really would suspect blocked carb jets.
It's not a big job to clear them. Take off the carb bowl, and have a wee look. You may have to take the carb off to get at them... I know not. Take off the carb float, and screw the jets out. They can be cleared with a wee fine wire. The purists say not to use wire, but don't say what else you are supposed to use if compressed air and solvent does not work.
If the motor has been rested a long time, it is helpful to pour plenty 50/50% oil/fiel mix into the crankcase down the carb throat. Let is soak to lube the crank seals. The two-cycle motor has crank seals, and they are vital. Often they get dry if the motor has been rested a longtime, and they burn when the motor revs to 3000 rpm the moment it starts.. let it soak for, say, 8 hours, then, WITH THE PLUGS OUT,turn the motor over to purge the 50/50% mix. Put the plugs in again.
With the jets cleared, carb back on, and some new gasoline in there, I will be surprised if it does not start.
I ressurected an old GT500A from 1977 that had lain for 8 years unused. The soaking of the crank seals was critical. The carbs were gummed out of sight. Now, some 6 years on, it is still running and has 150 psi compression. Maybe I got lucky. It vibtates like sin, but then they all do Sir.
All a two cycle motor asks is not to be thrashed when cold, and not thrashed out of sight at all when hot. Taken easily, they can last a long time. I know of one dude that had 169,000 miles on an old MZ 301 motorcycle, a communist design, and probably more by now.
Even if you start the motor for a few seconds every few weeks, they will behave.
They detest being stored unused, and often they don't forgive it without TLC, like the TLC above.
Good luck.
Rockter.