My question about whether you have Acceleration installed was actually so I could know if you are updated to FSX SP2. Acceleration automatically installs the service packs' material, which is necessary for the A2A aircraft to work correctly. You should be good there; I don't think this is the source of your problem.
First, be sure that you have the realism settings marked exactly like the Cub's instructions suggest, especially the part about disabling the automixture. The AccuSim aircraft bypass a lot of the stock FSX coding and with some of the AccuSim planes the engines will wheeze and pour smoke and even catch fire if you leave the automatic mixture enabled.
The AccuSim aircraft have persistent maintenance states between flights; if you broke your engine early on the plane will still be broken the next time you load it. To fix this, open the Maintenance Hangar panel (Shift+7) and click the overhaul button. That should reset your plane to a 'like new' condition.
Next, make sure you have gas in the tank. I think the load manager panel is Shift+3. I don't know why you'd have an empty gas tank so soon but this is an easy thing to eliminate as a problem so you might as well just look.

If the above conditions are met (Acceleration installed, realism settings not using automixture, the engine is overhauled and in good order, there is gas is in the tank) you should at least be able to autostart the aircraft. If the autostart (Control+E) doesn't fire up the plane, try switching to a stock plane and then back to the A2A Cub.
By the way, there is a 1.1 update patch for the Cub. If you haven't downloaded it yet, go to the A2A Simulations forum.