The particularities of cardboard and marbles would likely prevent it from being "self-aware", in so far as "self-awareness" requires that the machine be fed a large amounts of information regarding itself, through itself. How many kinds of sensors can you build out of cardboard and marble? I don't know. But probably not many, and not as good or abundant as those receptors present in mammals, like those which constantly feed data into our nervous system.
But yeah, if this isn't an actual problem, you'd probably have something self-aware.
I think the limitation here is that the amount of cardboard required would lead to some sort of gravitational collapse. Other than that, there isn't a limit to the number of sensors you can build out of cardboard and marbles.
But yeah, if this isn't an actual problem, you'd probably have something self-aware.