One thing that comes to mind when you say that you have to press the accellerator to get it to start is the Idle Air Control Valve (IAC).
I cannot see the fuel pump causing the problem that is solved by pressing the accellerator or the coils.
The IAC is a valve that is controlled by the computer and controls the idle speed when your foot is OFF the accellerator.
It bypasses the throttle plate that the accellerator is opening when you press on it.
The IAC is known for getting dirty and sticking.
So, do a search on IAC and see if you can come up with a picture of where to squirt some cleaner to clean it up.
My 2003 has a dual throttle and it is located in the one that is to the rear.
The hole to spray in is in the base of the throttle body, in front of the throttle plate.
This is a picture of it on my 2003, and you can see the hole in the throttle body to the right in the picture.
The black box on the bottom of the throttle body is the IAC.
You spray some throttle cleaner, I've used Berryman's B12 Chemtool in the spray can.
Seafoam Deep Creep will also give some cleaning (not as strong as the Berryman's) and also give some lubrication, which the Berryman's does not (lubricate).
It does not take much cleaner to do the job....spray it in and let it soak......connect things back up and start the vehicle.
Worth a try, as a can of cleaner and 20 minutes of you time is a LOT cheaper than coils or fuel pump.
Of course, if it has been a while since the fuel filter has been changed, then that is a good idea.......IF you have the version that has a changable fuel filter.
My 2003 does not, it is part of the fuel pump assembly.
Earlier Sienna did have a fuel filter in the engine compartment that you can change, I don't know when they changed over to the one in the tank.