Demosthenes said:
Well, it's not a total misreading of Kant, as some respected kantian philosophers are known by me to have thought that he said something of the sort.
I think you are at least on the right lines.
The way I would some up Kant's arguement is:
1) Time/causality are synthetic a priori notions.
2) If something is not part of a causal chain it exists outside of time.
3) If we follow causal chains back far enough then there must be a first cause.
This leaves us with a dilemma (an "antimony") which Kant resolves by noting that the "something" in 2) is necessarily a phenomenon for the argument to bite. Therefore we must assume that there exist noumena (ie. "things in themselves" which have no phenomenal exitence).
The argument
is idealist - what Kant called 'transcendental idealism'.
For me it is flawed most obviously because of the first assumption.
In any case I don't think it informs the debate about free will or responsibility. I could be wrong there. But its certainly not obvious what conclusions should be drawn from it.
My very quick take on the question of responsibility is to question the use of the word 'responsibility' in the first place. Is it a judgement or a statement of fact? We say we are responsible for something specific rather than responsible for actions in general, so it makes sense to judge things by their specific instance. Why are we so worried about moral judgements in general, when surely we should be concerned about the promotion of sociable behaviour?
In other words the question in the OP doesn't really interest me and I'm posting out of pure pedantry.