Well, I'm just going to go ahead and complicate things up for you. Also, I've added sort of a disclaimer to my last long post in this thread, in case anyone missed it.
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1. Atoms are composed of neutrons and protons (which have mass) and electrons (which do not)
Approximately right, however electrons do have a small mass, namely 9.10938215*10^(-31) kg(rounded). This is very important for a complete understanding of atoms.
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2. Electrons are the things that keep the nuclei (protons and neutrons) of atoms apart.
True, but it's important to note how they keep nuclei apart. Electrons are all negatively charged and negative charges repel each other. Thus, when an atom tries to near another atom, their electronic shells repel each other. Atoms have electronic shells because this is normally the most stable configuration (because every particle tries to achieve as little potential energy as possible. This requires an understanding of conservation of Energy and such).
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3. Stars send out light/heat radiation (which is basically escaped electrons).
Partially true, radiation can consist of electrons(this is called beta-radiation(with the Greek letter the forum doesn't support)) or out of other particles(alpha- and gamma-radiation). Light is a complicated thing, having both a matter and a wave aspect and consists of photons
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4. The atoms within a star have a limited number of electrons to send out through radiation.
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True, I guess, but most radiation from stars is created from combining protons or atoms to from new elements, giving of the excess energy as radiation(gamma). A star dies when it has combined all of it's matter into the highest ranked element it can create through normal solar nuclear fusion, Fe(iron). I felt I should add this because this statement seemed to hint at some misunderstanding on your part.
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5. When the atoms within a star run out of electrons through radiation - there is nothing to keep the nuclei of the atoms within a star apart, hence it collapses into itself to form what is essentially one gigantic atomic nucleus of protons and neutrons (a black hole).
Yeah, I guess the previous pretty much sums up my objections to this. Protons won't all stick together nicely, since they have the same charge and repel each other. Also, the Black hole article on wiki doesn't seem to make mention of atoms shedding their electrons and all sitting together with the same charge, which would be an extra ordinary event worthy of notice, so I'm afraid I think your theory is false.
I feel like I should add I'm almost 100% certain about most things in these post, since it's what I learned throughout my education. I might have messed up some details though, like forgetting to mention there are 2 kind of beta-radiation(electrons being beta minus).
Also, this was still an over simplified explanation, but you could talk about this stuff for years.
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I also have theories about how a 'black hole' reverts to a star, but again, I can't recall how much of that is my own amateur piecemeal science at work.
Feel free to share, I love toying in my head with these ideas.
EDIT: Fixed an image in a previous post, check it out, it's p cool.