I have the exact same model/age Fiat Stilo multiwagon. I have experienced a number of similar incidents with my car - suddenly experiencing a drastic reduction in acceleration & power for no apparent reason, accompanied by the engine fault warning light coming on. The problem normally resolves itself by the next day, although it has occasionally taken a little longer.
I did have a (cheaper) diagnostic carried out at a local Fiat dealership. They told me that the engine needed a new "Turbo overboost valve". I mentioned this to my local garage who do all works on the car for me & they weren't really sure what this was.
Anyway, I have not had anything done to resolve this and decided to live with the problem. To be fair it has not happened for many months now and I found it normally happened in a period of sustained damp weather (This may of course be entirely coincidental),
Stephen, May 2009