1999 Toyota Celica Problem Starting Car

I recently bought a 1999 Toyota Celica from a dealer and I'm already encountering a problem. After leaving my car in a idle state (Coming home from school, and not running it until I wake up the next morning) it tends to not want to start. When I turn the key, the engine will crank and the car will some what shake. The only way to get it to fully start is by stepping on the gas pedal (reving it). I changed the spark plugs, spark plug wires, distributer cap and rotor (Not the problem). After starting up my car in the morning and constantly using it for the rest of the day it seems to start up noticably fine. Do you have any suggestions of what the problem may be?

Thanks, Kyle.