Try cleaning the IAC valve first with throttle body cleaner, carbon builds up on the plunger and causes a hard time starting the engine.
Holding your foot on the pedal does not helps anything with the fuel system, AFAIK when you do that the PCM detects it and causes the system to stop spraying fuel to avoid a rich fuel mixture in the cylinders.
A bad fuel pump problem could be possible if you have to prime the system (turn the key on and off) several times before cranking the engine in order to build enough fuel pressure on the lines. This could also indicate a bad Fuel Pressure Regulator, remove the vacuum hose running to the top of it and inspect for any fuel dripping from it.
Oscar.