I think there is some denial of terms here, especially in the title question. Pedantically, anything that is not itself a star or stellar remnant, which orbits a star, is large enough that its gravity overcomes structural rigidity of its material to form a spheroid, and that has "cleared the neighborhood" of its orbit around the star, is a "planet". There is an upper size limit to what makes a planet as well; get too big and it starts exhibiting star-like behavior. More on that in a sec.
The limitations of our technology make it impossible to prove categorically that there are no masses fitting your description not orbiting a star (so-called "rogue planets" which, because they're not bathed in a star's light nor causing it to "wobble", would be very difficult to discern from cosmic background noise even if they were spontaneous emitters), but what we do know about our universe tells us that such a proposition is extremely unlikely because of the way matter accretes around large gravity wells like stars and other stellar/superstellar objects.
Turning more directly to your question, Jupiter is a well-known source of radio noise; the storms raging across its outer atmospheric layers produce charge differences orders of magnitude larger than those that cause lightning on Earth, which result in bursts of radio activity between about 18 and 32MHz (lying within the CB radio spectrum, but too faint to pick up from Earth's surface with this class of equipment). NASA's Radio Jove project collects and studies this noise for clues as to what's going on deeper inside the planet (and it makes for interesting listening to some).
Now, Jupiter's definitely a planet. It orbits our Sun, and one could assert that most of the energy we detect from Jupiter is, in some form, reprocessed solar energy. Jupiter, in the grand scheme of things, is also relatively small; we have found exoplanets orbiting other stars which are dozens of times Jupiter's mass. If they have similar composition and other characteristics, it stands to reason these objects would be pretty strong radio emitters (if they weren't being drowned out by their star).
In between about 13 and 80MJ (Jupiter masses), there is a grey area, or perhaps more fitting, a brown area. We've found celestial masses in this range of mass that do not exhibit true H1 fusion and so are not "stars" (that starts happening around 75 to 80 MJ), but do still produce self-sustaining EMR, through a sub-fusion process called deuterium combustion, which makes them more than planets. The most massive of these objects we have found to date (for which the mass can be reliably calculated) is Teide 1 at 55MJ. Not all of them orbit stars, though a few do, like Gliese 229B (somewhere north of 20MJ).
These masses are thus spontaneous EMR emitters, not planets and not stars; they are known as "brown dwarves", and are the closest known objects to your description. But, they still don't fit exactly, because they're made of lightweight materials that support fusion (or something like it), like hydrogen, helium and lithium. They're the true "stars that never quite made it" (Jupiter didn't even come close, despite many misguided statements to the contrary). Not all masses in this category are brown dwarves; for instance, USco1602-2401b, at 47MJ, is the most massive substellar object being called a planet (though we're not sure; it was only discovered this year, and at an estimated temperature of 4700*K while orbiting its binary system at a distance ten times the radius of anything we'd call part of our Solar System, there's something going on). Brown dwarves are only classed as such when we can be reasonably sure that the planet is massive enough, hot enough and made of enough fusionable materials that these pre-fusion processes are the most viable explanation for their characteristics.
This is the fundamental problem of aggregating enough mass to form a spontaneous emitter; it is extremely unlikely for there to be enough of anything in the neighborhood but hydrogen to form a body that massive, and as is shown billions of times across the heavens, when you aggregate enough hydrogen you get a star.
Let's take everything we've identified or think exists orbiting our Sun, that is made up largely of something other than hydrogen and helium (the Sun, Jupiter and Saturn are all primarily H/He with relatively small amounts of everything else), and put it all together. The two largest single non-H/He objects in the solar system are the Neptune and Uranus "ice giants", at 17 and 15Me (Earth masses) respectively. The largest collection of objects with an estimated mass is the Oort Cloud at about 40Me. The asteroid belt and Kuiper belt's total combined mass is less than 1Me, and the masses of all moons of the solar system are just over 1Me. Earth, Venus and Mars together are not quite 2Me. So, all together, these bodies would create a celestial mass orbiting the sun of roughly 75Me.
Jupiter is 317Me. Saturn is 95Me (including rings). The Sun is 332,837Me. Brown dwarves would range in the thousands to tens of thousands of Earth masses. If our solar system is typical of others in the universe, there just isn't enough of anything but hydrogen (and other lightweight fusionable matter like helium/lithium) anywhere near a main sequence star that could be aggregated to make a superplanet on the scale we're talking about.