1997 Mercury Villager Cold Start Issue

My wife's mini van has this problem.

Here is history that might help with the answer.
Before all these problems, I took the dealer's advise to perform "power flush" to transmission. Later, someone told me that power flush might damage something. Few months after the flush, here comes the problem.

Once, the car won't start. The only way to start it is turn the key and push the pedal at the same time. Ford dealer replaces some sensor. It seemed worked for a while. Then few weeks later, the fuel pump went out. It got fixed as well. However, the following problem seems to persist.

When starting the engine the very first time in a day,
it starts slow then within 2-3 second it would rev up to the normal condition. BY slow, I mean, it got started then dies down a little bit, then picks up again. This only happens the first time in a day. After that, it would start like it supposed to be for many hours after a short driving. I guess the problem only exists when the engine in completely cold.

Any advise would be appreciated.

Philip