Not to contradict the above answer but you do not need to have the layer you want to identify ticked. Well not entirely. If it is select then yes but the question seems to lead to interogating the data.

If you want to interogate the data click the i button. Ensure that in settings > options > map tools that you have selected top down in the identify box.

This works for intergoating data NOT selecting.

Sorry if i miss the point. Dont down vote if i have i will delete answer if it is wrong.

Not to contradict the above answer but you do not need to have the layer you want to identify ticked. Well not entirely. If it is select then yes but the question seems to lead to interrogating the data.

If you want to interrogate the data click the i button. Ensure that in settings > options > map tools that you have selected top down in the identify box.

This works for interrogating data NOT selecting.