For free will to exist two things must be the case:
1. In some situations there is more than one possible future.
2. Which future actually happens is a matter of personal control.
Determinism negates the first. So if strict determinism is true, then there is no free will.
But, even if there is more than one possible future, it is still possible there is no free will if it is the case that a person isn't the one affecting which future is actualized.
In the OP, it is possible that the 'choice' of whether to go to work is determined by previous events and that the only possible future is the one that actually happens. In that case, there is only an illusion of free will, not the actuality. To have free will, both the future where you go to work and the future where you don't have to be possible futures.
Now, with quantum mechanics, it is known the determinism isn't the case in the real world. it is often the case that the future value of a quantum variable is undetermined by its past. This allows for a 'randomness' that some take to allow for the possibility of free will.
The problem is that which future is actualized in a quantum event is NOT under the control of any person. This means that instead of choosing the future, the specific future is actualized by something other than some person. If anything, this is worse for free will than determinism.
The Libet experiments are often debated but I have a feeling they are often misinterpreted. The interpretation is that the feeling of choice happens after the brain signals that initiate activity. I find it far more likely that the delay is due to the feedback processing for pushing the buttons. Making a decision *and* watching a timer at the same time is not a way to determine what you were thinking when a timer is at a particular point: thoughts take time and evaluating the timer takes time.