Instead of just speculating about what our solar system would be like if Jupiter was a star, we decided to test it out. If you haven’t heard of it, there’s a program called "Sandbox Universe," which you can download on your computer. It allows you to create your own solar systems, and see how things would change if you added or removed planets, moons, etc. You can go to their website and purchase it for around $10 USD (or you can get it on Steam, a game client, for about $5). Personally, I think it's well worth the money; it is very fun to play with (I usually spend my time figuring out what it would take to destroy our solar system...fun times).
The impact of changing Jupiter into a star depends on a lot of different variables: How massive it is, how hot it is etc. You can enter in whatever factors you want.
WATCH: Sandbox Universe Simulation
For the first experiment, I changed Jupiter’s mass and density to that of the Sun. I’m not going to lie; the destruction was entertaining to watch. The moons of the planets that were closest to the new Jupiter-Sun, like Saturn, Uranus, and Neptune, were thrown in every direction, and they collided with…anything and everything. The asteroid belt was also destroyed—asteroids were thrown everywhere, pelting the inner solar system relentlessly with heavy impacts. In every simulation (no matter what factors I entered in for the new Jupiter-Sun), Earth was destroyed in one way or another. It either collided with other planets or one of the two suns. If Earth didn't hit something, it was thrown in towards the current Sun and ended up being closer to it than Mercury is today, which means that our planet (and all the life on it) would fry. In other simulations, it was ejected from the system to freeze in the blackness of the cosmic void.
In most simulations, Mercury and Venus were relatively unchanged (with the exception of getting pelted with asteroids and moons). This is because the influence of the Sun is far greater than that of the Jupiter-Sun, as the planets are much closer to the Sun; however, as was already mentioned, the planets in the outer solar system didn’t escape damage (not even a little bit). They either collided with something or were ejected from the solar system.
All in all, complete destruction when it comes to life on Earth, and the solar system was unrecognizable. Even if Jupiter was to evolve into a star in the beginning of the formation of the solar system, a relatively similar outcome would occur. A lot of material would have been pulled into the Jupiter-Sun, leaving a lot less material for planets, moons, and asteroids.