The only problems I have had with starting default type engines in FSX is with:
Fuel Valves closed
FSX engine start-up bug.
Neither of them apply to you if can't start it automatically with CTRL + E, because CTRL + E should bypass both these issues.
The fuel valves closed is common problem when trying to start engines manually
, and can crop up if you've used an add-on recently that let's you close the fuel valves, then switch to an aircraft that doesn't have them. Most default / simple aircraft don't have the fuel valves assigned to either a switch or a key, so you would need to first assign that FSX variable to a key. You can do that in the key assignments page where there is an entry called "Open/close all fuel valves". I set mine to CTRL + SHIFT + 5.
Regarding the FSX startup bug, again this only applies when staring engines manually
. If you create a new flight in free flight, and choose a piston engined aircraft like the the default cessna, you cannot start it with the mouse. It needs to be started with CTRL + E, then shut down, then saved, and then opened. Then you can start it with the mouse. However, this would not be the cause of your problem if CTRL + E works for you although it is worth a try to create a new free flight with the default Cessna, start it up with CTRL + E, then shut it down completely, then load the A2A spitfire and see what happens.
The only other things I can think of with your aircraft is fuel tanks empty, or dead battery, although with a dead battery nothing should be happening at all. Failing this, it's an installation problem, so re-install.
Let me tell you a little story about the Accu-sim B-17. I had three hours to myself and decided to fly from Murmansk to Stockholm. I spent the entire three hours trying to start the engines! Even when I managed to start an engine, the RPM would not respond to throttle input, and after a few minutes the engine would die and the plugs would foul up. I was convinced it was bug, and re-installed it, only to have the same thing happen again. I later found out from this forum that the reason was because the outside air temperature was -7 and I wasn't using enough primer, and even when I succeeded in starting an engine, I didn't have the Turbo's on to warm the incoming air so the carburettors were freezing up almost instantly, killing the engine. I did not occur to me to turn on the turbo chargers while idling on the ground...