FYI: The battery is only needed to crank the engine for starting. If the engine cranks but won't start, the battery is likely good. The alternator is used to recharge the battery. If the battery gets recharged while the engine is running, the alternator is likely good. It sounds like you did not need to replace either.
Basically, two things are required to start an engine that cranks. Fuel, fed to the engine from the gas tank by the fuel pump, and spark, generated by the ignition coils and fed to the spark plugs through spark plug wires. The spark is used to ignite the fuel and run the engine.
So, you need to check those two things.
Assuming you have gas in the tank and it's not contaminated (i.e. mixed with water or other substance), check to see if fuel is being sent to the engine. With the key on but engine off, you should be able to hear the fuel pump whirring at the back of the car. Under the hood, you can check if fuel is getting to the engine by a) you may be able to smell it, since the car isn't starting or b) poking the needle valve in the fuel rail.
You can check for spark by pulling one of the plug wires loose from the engine and while holding the wire with insulated pliers, have the engine cranked and see if you can get a spark to jump to ground (either a metal part of the engine or the plug from which you pulled the wire).
If you have fuel and spark getting to the engine properly, the problem could be with one of the engine sensors, such as crankshaft or camshaft, or with the engine computer.