If you took a bunch of asteroid materials (say carbonaceous because otherwise boring) and cloned up a sun-scale mass (probably below sun size) of them, they'd turn into a star. Depending on the kind of asteroid and its elemental makeup all sorts of weird stuff might happen. There's a colossal amount of energy produced by putting that much mass nearby. Even if it starts out cold and not moving, gravitational energy released as it compacts into a sphere will make it very hot.
- Lots of light elements: mass collapses -> ignite fusion -> A regular star, for a little while at least.
Deuterium fusion begins at $13 M_J$ and lighter bodies are normal planets. Hydrogen fusion begins at $75−80 M_J$ (bodies that burn deuterium but not hydrogen are brown dwarfs), but I (editor) have heard that with bigger amount of elements heavier than helium even lighter stars could ignite.
- Mixture of light and heavy elements -> ???? (but probably explosions as you skip straight to the supernova stage very quickly)
- Many heavy elements: Ignition is impossible, so we will end with degenerate matter.
At 1 sun mas, white dwarfs are probable. According to Wikipedia, helium fusion is possible already above $0.5 M_\odot$, but fusion of carbon, oxygen, neon and silicon happens only in very heavy stars. Iron is most stable and one cannot get energy from it with nuclear reactions.
Chandrasekhar limit for white dwarf mass is $1.39 M_\odot$ and than we may end with a neutron star. Tolman–Oppenheimer–Volkoff limit for neutron star mass is $1.5−3.0 M_\odot$, and heavier bodies without fusion become black holes (unless some exotic stars can exist).
Elements heavier then iron would be a case without precedence. They could undergo some strange nuclear reactions between fusion and fission.
Finally, among others, the last common element, uranium, undergoes well known nuclear fission and explodes above critical mass (mere kilograms). It could shine similarly to typical fusing star even for only planetary mass if only the mass was big enough to prevent shattering.
Unless you have very weird asteroid materials your giant planet is going to burn deuterium for at least a while. It's not the most luminous (but it is magenta) but adding a second solar mass to a solar system like ours is going to wreck some stuff. Expect to lose planets to interstellar space, see others crash into each other or swap orbits or disintegrate. If Jupiter hit this new gas giant/rocky weird thing at any speed expect, uh, fiery cataclysm.
In short: A lot of really weird stuff but you probably can't live on it. Either it'll be too hot or it'll collapse into a white dwarf, a neutron star or a black hole.