Even though a brown dwarf can't achieve stable hydrogen fusion, that doesn't mean it is incapable of sustaining any form of nuclear fusion at its core.
The dividing line between brown dwarfs and gas giant planets is generally considered somewhere between 10 and 14 times the mass of the solar system's most massive planet, Jupiter. That means we shouldn't find a planet with more than around 13 times the mass of Jupiter.
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This is because, at this mass, celestial bodies are capable of triggering the steady nuclear burning of deuterium, a "heavy" form of hydrogen. Rather than having a nucleus of just one proton as does "standard" hydrogen  —  the universe's lightest element  —  deuterium has a nucleus of one positively charged proton and a non-charged neutron. This is the reason brown dwarfs can have a faint glow.
"The major difference between brown dwarfs and planets is their mass and the occurrence of deuterium burning," Grieves said. "At larger masses, an object will have a high enough internal pressure and temperature to burn a majority of the deuterium that was initially present in the object."
The dividing line has been set so brown dwarfs are classified as objects that burned 50% or more of their initial deuterium. Yet that line is blurry, because other characteristics beyond mass  —  like the fraction of helium in a celestial body  — could result in the burning of deuterium.