Lack of spark is definitly a problem. I'm not familiar with the twins. Does it have one or two point sets/coils? I'd say trace the coil wires to the points, make sure there are no loose/broken joints. Make sure the wires aren't pinched.
Once you get spark, double check that the spark is deliverd at the right time. The points should open when the firing piston is near top-dead-center. Search for "static timing" on the site here for instructions.
If you have spark and it's timed correctly, the next thing is fuel. Smell the exhaust for unburned gas. Check that fuel is flowing to the carbs. Drain the float bowls, hopefully they have drains.
If you have a well-timed spark with a gas and it STILL doesn't fire, then you need to look into fuel/air mixture (read: carb rebuild) and compression.