Well, I'm not an astonomer or a cosmologist, but I will take a shot at it.
By definition, a protostar is a large object that forms by contraction out of the gas of a giant molecular cloud in the interstellar medium. The protostellar phase is an early stage in the process of star formation. For a solar-mass star it lasts about 100,00 years. It starts with a core of increased density in a molecular cloud and ends with the formation of a T Tauri star, which then develops into a maiun sequence star. This is brought about by the T Tauri wind, a type of super solar wind that marks the change from the star accreting mass into radiating energy.
Most scientists agree that our solar system formed at the same time, all of the planets and the sun. When the sun was accreting material, it was accreting gas molecules, when Jupiter was forming, it was accreting smaller clumps of rock which became larger and larger. Once Jupiter became a certain size, and accreted all of the material available it began to accrete the gas that was available (as it was now denser and had become gravitationally viable.) So, as Jupiter formed, it missed out on the symetrical availability of gas of which the sun took advantage. Actually, a single sun in a system is somewhat of an oddity. Odds are, usually, binary systems are the norm. Our solar system actually had a better chance of having two much smaller suns, than having a larger main sequence star, and four gaseous planets.
I understand that Jupiter would have had to have been any where from 20 to 80 times larger than it is, for it to have "turned on" but I don't know for certain. Jupiter and the sun share almost identical amounts of Hydrogen and Helium in their gas make up, I think about 80 to 20. Jupiter just missed out on the availability of exclusively gas molecules in it's advent, I think. So, by definition, it wouldn't be considered a protostar.
Go Cyclones :yes: