Well...first it would have to gain a lot of mass, about 20 times or so it current mass. Only then would the temperatures in the core of Jupiter which are now about 57,000 K, get into the roughly 1 million degree range needed to start thermonuclear reactions involving deuterium. In the movie 2010: Odyssey Two, presumably the 'monoliths' provided enough of this mass, however, as the mass increased, the orbits of the satellites would become smaller and smaller, and the outer layers of Jupiter would begin to expand out in response to the heat being generated in the core. The Jovian satellite system would be wiped out, and Jupiter would glow as a red star, not a dazzling bright sun-like star. If the mass of Jupiter became sun-like, the orbits of all the planets would change catastrophically and the earth would be ejected from the solar system. Guaranteed!