This is the definition of free will you gave:
my definition of free will is the ability of a person to overcome his determining factors, most of which he is unaware of. Such factors as genes, experience and environment and probably countless other ones we can’t possibly know about.
Now compatibilism proposes another definition:
Free will means that persons are able to act according to their wishes and beliefs.
Now at the moment you say “yes, but your wishes and beliefs are determined” you are again applying your definition. So what you are saying is that your definition is the only correct one. Now on basis of which criteria can we decide which is the correct definition? You say on one side that your definition is the correct one, but at the other side say that it does not exist. Is that then a correct definition? What is the correct definition of a circle with the form of a square? It is obvious immediately from the beginning that a free will as you describe it does not exist.
But in daily life we are very well able to distinguish between actions that are voluntary or coerced. So the question is then, if we can make this distinction, on what it is based. And compatibilism offers its own definition of free will. And this definition needs determinism (at least to a certain level) to be true. If determinism would not be true, there would be no connection between our actions and our wishes and beliefs, and our wishes and beliefs would be unrelated to our biological and biographical past. So to accentuate once more:
Compatibilist free will presupposes determinism to be true.
Compatibilism is not looking for some magical hole in the causal fabric of the universe, nor is it looking for some middle ground where libertarian free will and determinism can coexist, no, it needs determinism. So any argument saying “But we are determined, so we are not free” completely misses the point of the compatibilist definition of free will, and you are applying your own definition again.
So the whole quarreling is not about if we are free or not, but what the correct definition of free will is, and all the time you only consistently argue from your own definition. And I say your definition is wrong because it is incoherent, is not consistent with the fact that determinism is true (at least for the relevant processes), and is not able to account for the distinction we can make between free and coerced actions (both are determined).