Hi,
If you've had the battery checked and they say it's fine, then that's a start. If the alternator was the problem you would have had either a battery light on all the time when the engine was running, or coming on shortly after starting. This is because the battery would not be receiving enough charge. If your timing belt/chain has slipped, you would have known about it when you had the engine running, it tends to write off the engine, (bent valves etc). You should not have to apply full throttle to start a car, so don't push the pedal to the floor. I'm not familiar with the car as suspect you're American, but get someone to check the strength of the spark at the spark plugs.
Cheers now
Ken Chapman
June 2007