You're conflating a whole lot of things there, not to mention presenting as mutually exclusive two notions which aren't.
First of all, nothing about "natural rights" implies that these rights are "god-given" or "inalienable." (Although folks have certainly said both, which I'll get to in a moment.) Natural doesn't intend to imbue with a supernatural authority, nor to imply that such rights are ipso facto inviolable. Natural merely suggests that the rights are an extension of the basic, shared sense of justice which all societies evince.
Keep in mind, I'm not talking about the complex moral codes which have evolved over time, influenced by different religions and a host of other factors. I'm talking about the very basic stuff: you can't just come and kill me, because if you do I will try to kill you back to prevent that. Likewise, if I try to kill you I should expect you to try to kill me back to stop that. If I'm holding this apple (which I picked from a tree on my homestead), and you hit me to take it, you should expect me to hit you to take it back. And since we all share in common these expectations, we agree to organize our society around them, and to take some collective interest in seeing them maintained (and met) even in cases of power disparity, etc.
This is all that is meant by natural right: people will treat as owned property they acquire through their own efforts, defend life (and that property), and engage in voluntary relationships with other people. Rather than seeking to impede these natural and inevitable human endeavors (as some governments have and do), government should – if it is to do anything at all – ensure that they are respected equally for all its citizens.
As to the concept of "god-given" rights, I find it uninteresting and have rejected it (being an atheist). I won't give it further consideration.
The putative "inalienability" of rights is an attribute distinct from their being natural. Furthermore, the objection to "inalienability" is moot as nobody in the entire history of intellect has ever intended to argue that rights are not possibly violated – and indeed are not actually violated all the time, by governments and criminals alike. When someone speaks of the right to self-defense as being "inalienable", they don't mean government is unable to pass and enforce legislation against it. What they mean is that, when a man's life is on the line through no fault of his own, no law can stop him from doing what it takes to survive, and any law which imprisons him after the fact for doing so is simply in opposition to right.
That rights should – must – be defended is a reality not exclusive with these notions. In fact, I'd say we all agree unquestioningly that rights need to be actively defended (or won) to be exercised with impunity.
It's quite a leap from there, however, to accepting that government grants us rights, or is capable of doing anything more than – at its very ideal best – protecting them (say from criminals or foreign aggressors).
My rights – to life, property, and liberty – exist. Obviously.
I exercise them because I (we) haven't let government punish me for doing so.
(How's that for an understanding of rights, TheYankeeMarshal?)