Dissmissing features based on correlation with target variable
You've really got a classification problem on your hands, not a regression problem. Your target is not continuous, and Pearson correlation measures a relationship between continuous variables really. That's problematic enough to start.

Low correlation means there's no linear relationship; it doesn't mean there's no information in the feature that predicts the target.

I think you're really looking for mutual information, in this case between continuous and categorical variables. (I assume your other inputs are continuous?) This is a little involved; see https://stats.stackexchange.com/questions/29489/how-do-i-study-the-correlation-between-a-continuous-variable-and-a-categorical

If you're attempting to do feature selection then you could perform a logistic regression with L1 regularization and select features based on the absolute value of their coefficients.