Define free will.

 Sorry to be pedantic, but I need to know exactly what you mean in order to answer your question effectively.

When you speak of making choices without external coercion, do you mean that the "decision making device" -- whatever it is -- operates independently of the environment?  In other words, supposing that after writing this post, I decide to go to the kitchen and grab a beer.  (I've been thinking about it for some time, and haven't yet made up my mind.)  Will my decision be made by some "decision making device" that operates arbitrarily outside of the sense data that I cannot help but perceive and the memories, perceptions and experiences that are part of my memory?  Or, are my decisions the result of an "algorithm" that is the sum of my genes, memories, and current state of empirical awareness?

 Well, if you're avoiding answering the question of determinism, then you're preventing me from answering your question.

 Ok.  Now we're getting somewhere.  Pardon me for drawing this out, but I really didn't want to have to explain all this.  Since you know what you're talking about, I think we have a good place to start.

I should warn you that I don't believe in what most people think they mean when they say "free will."  I am not necessarily a strict determinist.  That is, I don't know that I believe given exactly the same external stimuli, a person in the exact same place in time would make precisely the same decision a million out of a million times if we ran time back and watched.  I don't think anyone can say for certain whether reality is like that.

Having said that, I don't think the distinction matters.  Perhaps on a quantum level, the universe is at least partially truly random.  If that is the case, perhaps the universe is not 100% deterministic.  Nevertheless, I think we can say that practically speaking, we cannot help but make the decision we feel is the best decision to make.  Our current state at any instant is not under our control.  It is, as you say, a product of our bodies (as dictated by our genes) interacting with our environment.  Neither our genes nor our environment is under our control.  We reach a state of awareness of desire AFTER our brain has completed the "calculations" leading to that state.  (That is scientifically proven, if you didn't know.)

So... the traditional view of free will -- the ability to arbitrarily make any decision whatsoever -- is bunk.  We can only decide that which our current state of existence allows, and we will only reach the single decision which our current state of existence deems best.  So, rather than speak of free will, I like to speak of autonomous decision making.  That is, there is no entity other than ourselves making our decisions.  Whatever I decide, it was my brain that did the deciding, and no other.  There is no homonculus in my brain.

Now...

Supposing there is an entity with omniscience.  That is, a being which possesses total awareness of every conceivable piece of data from the beginning of the universe until the last movement of the last subatomic particle.  (Nevermind that this state of existence is philosophically impossible.)  Supposing that such a being existed, we could speak of autonomous decision making in two ways:

1) With regard to the omnicscient being, there would be no autonomous decision making whatsoever.  Even the being himself would be bound by his own knowledge, and could not help but do what he was destined to do at every given instant.

2) For beings not possessing omniscience, the question is a little more complicated.  Did the creature possessing omniscience create reality?  If so, then it's pretty hard to say there is any autonomy.  If he is not the creator, is he trapped within the universe?  If so, does he interact with it in any way?  If he is just a motionless observer, then his knowledge has no measurable effect on the universe, and so we may freely speak of autonomous choice in any beings not possessing omniscience.  That is, even though there is a motionless being who knows what choice will be made, there is no mechanism within the choosing being that can access this information, and the choosing being is not being externally influenced by the motionless being.  For all practical purposes, the motionless being does not exist.  It is just a data storage facility.

What I'm getting about in a round-about way is that the question of omniscience and free will is broken because the definitions of both concepts are problematic.  Until we have a clear understanding of PRECISELY what both mean, and if both are even workable in a hypothetical... we're just talking in circles.

 If a being knows what he is going to "choose" in the future, then that is equivalent to 'perfect determinism', in that there is only one possible future sequence of events.

This is more 'deterministic' than scientific naturalism, which takes into account complexity theory ( 'chaos' ) and quantum mechanics, and says that the future is not knowable or predictable in precise detail. In fact, it says that certain categories of process have extreme or even virtually infinite sensitivity to initial conditions, may have very different outcomes if it were somehow possible to restart from the same initial conditions. Of course rewinding like that is intrinsically impossible due to quantum uncertainty.

'Determinism' in the classical sense is an abstract concept that doesn't apply to reality, which is more subtle and complex.

Of course, that is a trivially true observation.

I said nothing about "one actual sequence of events" - obviously there is only one actual sequence, since the universe is not going to be re-run, and I think could not be, in that hypothetical sense.

Of course you have options, and your choice is going to 'determined' by an immensely complex set of influences, most individually of negligible significance, and many having an element of intrinsic randomness and/or unpredictability, dominated by the proximate state of your mind, mood, urges, or impulse, etc, IOW, YOU. The only alternative I can conceive of is a choice not affected by anything, even your own thoughts, or purely random.

The biggest problem with the idea of 'determinism' is that it conjures up a mechanical sequence of one event rigidly defining the next in a sequence, which is a misleading mathematical abstraction, not a very good approximation to reality.