Fuel, make sure fuel is flowing to the carbs, take the nut off the bottom of the bowl, Drain some fuel in a drip cup and make sure it flows in, both carbs.
Check the plugs, Check the spark. (check the spark with plugs you know fire, not necessary the ones in the machine)
If no spark, check connections, check stator, flywheel, make sure key is in Crank, could be sheared and your are 180 degrees out.
Check coolant - O-ring blown? Check for leaks at the head Gasket/Base Gasket.
Check compression.
Really sounds like an an electrical problem or fuel problem.
There is like 9 different possible electrical problems. Check to see if on the right side of the air box, your wires hit your pipes and melted them causing a short? Just thinking outside the box here.
Adam