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Free will is usually a poorly defined term. For many, it's an overly strict definition that, as you've described, becomes impossible. But take the definition "the ability to act at one's own discretion.". The fact that your discretion is predictable or random or both doesn't make it not your discretion.
Let's say I have 4 robots and a maze. The only choices the robots are able to make in the maze is to go left, right, forward, or back. 
The first robot has a program it will follow. The program is complicated enough that an observer would have a hard time figuring out the decision tree. 
The second robot will base its choices off of the random particle decay of a chunk of radioactive material inside the robot. 
The third operates with both. It follows a program, but the program is influenced by the particle decay. 
The fourth is a black box, with no way of knowing what is inside the robot or what factors influence the path the robot takes. 
These four robots are released into the maze without any markings showing which is which. After watching them operate for a certain amount of time, do you think you could reliably tell which robot is which? >

Of course.
That's how PacMan works. >

Your realization about determinism/randomness is correct and is a very old realization in philosophy.  
Your conclusion that this makes free will 'impossible' is malformed, in the same way that 'free will' as a concept is malformed.
The standard response to this realization is to say that our intuitive notion of free-will is incoherent and needs to be amended into something that makes sense, rather than to say that free will is 'impossible'.  
Basically, the intuitive notion of free will which this realization argues against isn't even well-formed enough to be possible/impossible, it's just underdefined and vague.  
The most popular coherent notion of free will is compatibilism, which basically says that free will is measured by how much an agent is able to act based on it's own internal impetuses and desires and intentions, versus how much its actions are constrained by outside forces.
This formulation of free will is independent of the determinism question - the agent can be guided deterministically by factors internal to itself, it can be constrained by random assaults from outside itself, whatever.  The definition instead just focuses around how much self-determination the agent has, how much it's behaviors and outcomes are self-motivated rather than externally-determined. >

The problem I have with compatibilism as you're describing it and as I generally understand it is indeed that all it's doing is redefining a term to mean something that most people don't seem to mean by the term. Although it's why I tend to like to clarify with say "libertarian free will" which rather obviously doesn't seem to exist.
However, the idea that free will can be determined seems rather to fail most intuitions on what we're trying to get at with free will. I think. And as such, I guess I need more information on how redefining free will in that way is useful - i.e. how do we expect people to use the term? Why not just stop at the idea that free will is an incoherent intuition.