What does it mean for there to be no correlation between phylogenetic independent contrast?
Your first option is the correct interpretation. The correlation you observe in the raw data is the effect of phylogeny.

Without using PICs, you might expect to see phylogenetic autocorrelation, i.e. your raw data correlate as a function of the amount of shared evolutionary history between different species. Using PICs is one way of testing whether the correlation still exists when the effect of phylogenetic autocorrelation is removed. This is exactly what you observe—you see the correlation in raw data (which are not phylogenetically independent) but it disappears when you use PICs. Without knowing any details of your study beyond what's in the question, it sounds like a textbook case of phylogenetic autocorrelation.

The PIC method originates with Felsenstein (1985). I'd encourage checking that paper out for further details on the method and interpretation of the results.