There are some caveats here that need addressing.
1. As snorkack asked, "how do you define 'star'?"
I am unable to quickly find a rigorous definition of a star, but I believe a star is usually considered a large, luminous object held together by its own gravity and that has the ability to fuse hydrogen in its core (or did so in its past). The last part, the ability to fuse hydrogen in its core, is important because it let's us make a distinction between 'stars' and 'things-that-look-kind-of-like-stars-but-aren't-quite'. Brown dwarfs are formed in exactly the same manner as stars and have the same composition, but are unable to fuse hydrogen (protium) in their cores because they are not massive enough. They also fall into the classification of 'sub-stellar objects', which are objects less massive than stars.
2. What are stars usually made of?
The typical star is composed of about 71% hydrogen and 27% helium (by mass). So around 98% of the matter making up a star is hydrogen or helium, the two lightest elements.
3. Why are these two things important?
We'll get to that. Right now actually.
These two things are important because of how stars get the energy they need to stave off collapse for millions to billions of years. They get it through nuclear fusion. Primarily the fusion of hydrogen. The stage of a stars life during which it fuses hydrogen is known as its Main Sequence Phase and is typically the longest part of a stars life.
As I said above, stars are composed mostly of hydrogen and helium. These two elements release a lot of energy from fusion and the products of their fusion also release lots of energy. At least up until you reach the elements of iron and nickel. Because of the way the opposing forces of electromagnetism and the strong force interact with nuclei, iron and nickel are the 'end point' for both fusion and fission. Fusing these elements together takes energy instead of releasing it, as does splitting them apart.
Now, so what? Well, the OP is asking the question,
"Does this mean that any type of matter you put in space regardless of what it is, given the correct conditions will turn into a star?"
Given the definition of a star I gave above, and the knowledge that elements heavier than iron/nickel do not release energy upon fusing, the answer is
no. If I put 5 solar masses of the element lead into a small gas cloud, which then collapsed under its own gravity, that material would not turn into a star. Oh it would collapse and shine like a star for a while, but it would not be a star under the definition I gave above. And it wouldn't shine for very long either (relative to an average main sequence star). Fusing hydrogen releases a substantial amount of energy. Far more than the gravitational potential energy released by our lead star over time. GPE is important because it is the sole source of energy available to a non-fusing, collapsing body like our lead star.
But, if you're definition of a star is different from mine, or if you're creative enough to 'stretch' the definition above, then you might be able to answer with something other than "no".