Brown dwarfs are cosmic objects from which we are still learning things all the time. Even so, scientists have been able to distinguish what differentiates a brown dwarf from a giant planet, or from a normal star.
Brown dwarfs are categorized as failed stars, They're cosmic bodies of huge mass and size, which are unable to produce the precious nuclear reactions characteristic of the interior of normal stars. The power and energy of a star come from the nuclear fusion reactions on its core, reactions that release tremendous amounts of radiation in the form of light and heat. But for these reactions to happen, the cosmic body (i.e., the star) must have a great mass concentrated in a reduced radius, so that the pressure on its interior is enough to force hydrogen atoms to fuse with each other.
It is widely accepted that, for hydrogen nuclear reactions to be triggered on its internal structure, the cosmic body should be at least 75 times of Jupiter mass. A body with a superior mass than that might be classified as a star. But below that limit, the body is too light to undergo nuclear fusion of hydrogen. However, not all hope is lost for such objects. Deuterium is an element capable of experiencing nuclear fusion at lower pressures and temperatures than hydrogen, thus being the main fuel burned on the interior of brown dwarf stars. And which is believed to be the lower mass limit to trigger deuterium fusion? Around 13 Jupiter masses.
So Jupiter does not only lack the mass to become a natural nuclear reactor, but it is far below the mass needed to do so. Besides, Jupiter is too cold to be a brown dwarf. The heat emitted by nuclear processes is a good way to know if something explosive is happening at the core of a cosmic body, and in the case of Jupiter, its core burns at around 24,000 degrees Celsius (43,000 degrees Fahrenheit). That seems hot, but is actually several orders of magnitude below the temperature reached on the interior of most brown dwarfs, which is near 3 million degrees Celsius (5.4 million °F).
In short, if Jupiter was a brown dwarf, it would be so hot, bright, and catastrophic for the current arrangement of the Solar System.
