I wouldn't worry too much about Jupiter or Saturn turning into a star. Even if we did start a fusion reaction in their core, they would flicker out after a small burst of light. They are about the right diameter for a small star, but they just don't weigh enough. Jupiter is about 75 times too light for a sustained fusion reaction, and Saturn is about 250 times too light.
It is said that the Mars people tried it a long long time ago. It didn't work for them either.