If you ignite Jupiter, it would quickly go out again. It doesn't have the mass to sustain fusion, even if the fusion somehow got started in the first place.
People often misunderstand a fusion reaction as being a naturally escalating or upward-trending reaction like the fast oxidation (combustion) reaction that we are used to, in all its forms - be they a simple slow fire in open air or some semtex/TNT/dynamite exploding. In fact, fusion reactions are very loath to occur, it takes a lot of effort to sustain the fusion. Vast temperature and compression, which must not only be present at the start, but for as long as the fusion is to continue.
In nature, when you get sufficient mass together, nuclear fusion starts automatically, due to the combination of extreme compression and temperature at the core of the mass reaching the critical point. But it requires a lot of mass, more than Jupiter has. It would take at least 13 times Jupiter's mass to sustain fusion of any kind (deuterium fusion), making a brown dwarf proto-star, and 75 - 80 Jupiters to form a "proper" main-sequence hydrogen-fusing star.
Even if you could somehow artificially cause fusion to start in Jupiter's core, the moment the artificial stimulus was removed, fusion would cease. It doesn't have the gravitational compression required.