What conclusion can I get when the variable is influenced by other but there isn't any correlation?
First of all as your target value is continuous so it's a regression problem.
If the correlation doesn't give desired value it means there exist no linear relationship between variable and target variable you should look into mutual information.
Also, while interpreting a relationship, one should be careful to not confound correlation and causality, because although a correlation demonstrates that a relationship exists between two variables, it does not automatically imply that one causes the other.
So if you increase the values to get positive correlation of that variable with target it might not necessarily increase the same as there might exist a confounder.
Mutual information versus correlation