What can a star be made of?
A star's composition is limited by the elements that exist in significant quantities in the universe. These include primordial elements - hydrogen, helium and lithium - as well as heavier elements formed through nucleosynthesis in stars, supernovae and certain rare processes like cosmic ray spallation. This narrows down our options considerably; hydrogen, helium, oxygen and carbon are the four most abundant elements, by mass, in the interstellar medium. Radon, to use one of your examples, simply doesn't exist in significant amounts.
We also can't have molecules like ammonia (to use your example) as part of a fusion pathway. At the high temperatures at which fusion takes place (well over $\sim10^6$ Kelvin), molecules aren't even able to form; the metals that do exist in stars, like titanium oxide, are only found in the cool stellar atmospheres of the least massive stars. Even molecular hydrogen can't survive in the core of a cool star, let alone a star hot enough to fuse heavy elements.
We're even further restricted in our choice of elements because not all fusion reactions are exothermic, or energy-releasing. Famously, iron (and nickel) fusion consumes more energy than it releases, although it still occurs inside the most massive stars for very brief periods of time. We need our star to be supported by exothermic nuclear reactions. At typical temperatures in a star's core ($\sim10^6\text{-}10^9$ Kelvin), several types of processes dominate in different regimes. The elements typically fused are carbon, neon, oxygen and silicon. Other elements aren't going to be able to release energy in significant amounts through realistic fusion pathways.
Interlude: The alpha particle problem
One issue here is that many of these reactions either produce or consume hydrogen or helium. For example, one of the main oxygen-burning processes produces silicon and helium:
$${}^{16}\text{O}+{}^{16}\text{O}\to{}^{28}\text{Si}+{}^4\text{He}$$
In fact, helium nuclei (also known as alpha particles) play key roles in the fusion of many of these heavy elements, including the production of nickel and iron. This means that you do need some helium in your star for fusion to be significant.
How can you form a heavy-metal star?
Your best bet is to try to make a star out of one of the lightest stable, easily-fusable metals: carbon. It's a reasonably common elements that's produced regularly by massive stars, and the interstellar medium is enriched with it by supernovae. Furthermore, carbon fusion can happen at temperatures just under $10^9$ Kelvin - easier to attain that the conditions required to fuse neon, oxygen or silicon.
At low carbon abundances, when helium is present, the dominant pathway is
$${}^{12}\text{C}+{}^4\text{He}\to{}^{16}\text{O}+\gamma$$
where an oxygen nucleus and a photon are produced. However, when carbon is much more common, a different net reaction occurs:
$${}^{12}\text{C}+{}^{12}\text{C}\to{}^{20}\text{Ne}+{}^4\text{He}$$
creating neon and an alpha particle. This is the reaction most likely to happen in your star.
Before trying to form a star devoid of hydrogen and helium, I think it's instructive, for a start, to look at extreme helium stars, part of a broader class of hydrogen-deficient stars that includes R Corona Borealis (R CrB) variables and AM Canum Venaticorum (AM CVn) stars. These are all stars with essentially no hydrogen; instead, they're dominated by helium envelopes and cores of heavy metals. Extreme helium stars, in general, form through one of two types of processes:
- Double-degenerate mergers, where two white dwarfs merge and the resulting product is hot enough to undergo fusion. For instance, the most likely model for the formation of R CrB variables and some extreme helium stars comes from the collision of a $0.6M_{\odot}$ carbon-oxygen white dwarf and a $0.3M_{\odot}$ helium white dwarf.
- Shell fusion processes, such as a late thermal pulse or a dramatic shell flash, that involve the rapid conversion of hydrogen into helium, leaving behind a highly hydrogen-deficient star. Obviously, this requires a progenitor with non-zero hydrogen abundances, but the result clearly has negligible hydrogen.
You might be wondering why I bring these up; after all, the products still have helium. However, it seems reasonable that analogous processes could happen that yield stars deficient in helium, too. Let's look at what happens if we consider the double-degenerate model - with a twist. If both of our white dwarfs are carbon-oxygen white dwarfs, deficient in helium, there's the possibility that a merger could form a star that is now purely heavy metals.
The problem is that to produce the white dwarfs required for the collision, you need progenitor stars of intermediate masses (say, $\sim5M_{\odot}$). Massive progenitors may yield massive white dwarfs, and so these carbon-oxygen white dwarfs could be $\sim0.6\text{-}0.7M_{\odot}$, meaning that the resulting product will be near the Chandrasekhar limit and thus highly unstable. It shouldn't be a surprise that white dwarf mergers are now being studied as the progenitors of many Type Ia supernovae.