The a, b, and c' paths are significant but the c path is not. What does this mean? I did bootstrapping and the indirect effect is within the confidence intervals and the intervals did not include zero.
At the first glance, it looks like you have a full mediation, according to the mediation logic. In other words, mediator fully mediates the relationship between IV and DV.
I am cautiously writing since I do not know the specifics. If you have zero order relationships between IV and DV, direct relation of IV to DV is significant and you have a significant indirect effect of IV on DV then you have a full mediation. If you do not have a significant c relation betw IV and DV, there should not be a mediation according to Baron & Kenny model of regression. Yet it is regarded as outdated in some respects. I think you need to look up reporting templates (statistical cookbooks) suitable for the software you used for the exact type of analysis that you have used, (Hayes's PROCESS macro, or SEM, ...?).
Edit: A quote from the paper Ewalds-Kvist shared indicates that you may not be able to proceed into the mediation if there is no zero order correlation between IV and DV: "The results revealed that there were positive and significant correlations between any of two variables, which suggested that further analysis could be conducted."