When you say you have to hold the gas pedal down to get it to start, are you just holding it enough to open the throttle valve a bit, or do you have to hold it to the floor? If just a bit, you might have a throttle plate that is carboned up on the back side and needs a good cleaning. If you hold it all the way to the floor, that will put the car in "clear flood" mode which shuts off the fuel injectors while the engine is cranking and would suggest you have one or more fuel injectors that are leaking fuel in to your cylinders, and after the car sits for 20 minutes, enough fuel has leaked to flood the engine.
-Rod