Have you confirmed that the belt is indeed turning when the engine is being cranked? A partially opened valve will allow fuel to be drawn in the cylinder and then of course it will fire ... or sound like it's trying to start. Another thing to check is if it's getting enough fuel. Possibly clogged or malfunctioning injectors. A bad crank sensor is possible. Although a car will run with a bad cam sensor, just not all that good. A sure way to tell if it's a fuel problem is to squirt alittle (not much) starting fluid in the throttle body (or any highly flammable carb cleaner will work as well ... hell WD40 has started a vehicle for me once) If the car will idle for a second when that is introduced, it's a fuel problem and could be as simple as a clogged fuel filter. If it doesn't react any different, it's an ignition problem more than likely and as long as the timing belt is ok, then I would check the crank sensor. Of course all of this is merely suggestions and maybe you can take something useful from it.
Good Luck.