How to check if the dataset contains sufficient information to predict a continuous variable
You are describing something that you can create a series of scatterplots for. Hold your dependent variable constant and then just run scatterplots against all possible features and see what comes out. You can visually determine what makes sense (or at least what makes sense as a starting point) and then go from there. 

Also, don't forget that this is where you will also need to apply some of your own knowledge around transformations. Just because a scatterplot isn't obvious doesn't mean that it can't be used