Is it really possible to give intrinsic motivation to students?

So I was sitting at UCI and it was approaching 10 pm on a Thursday night while I worked on an assignment for one of my MAT II classes and I was thinking what makes me motivated to take the initiative to stay this late at school just so I can finish an assignment when I didn't need to be there doing it at that very moment. I have intrinsic motivation to learn, but how do my students who have no motivation to learn gain this same type of intrinsic motivation? I can't give it to them, that would be an oxymoron. I have mentored, I have tried extrinsic motivators that don't seem to last once the incentive is taken away. I am at a loss. I understand that there are strategies that work with some students, I just haven't been successful with my students this past year. During my student teaching I was successful at motivating my students using the strategies above, but this year in Inglewood I came across almost 80% of my students who had absolutely no motivation what-so-ever. This could be an anomaly, but I think it is a majority of factors that cause students to be unmotivated. I just am looking for answers on how to change that. I understand that people have different wants out of life, but I do not understand how refusing to learn can solve anything in life. All I want to do is help my students, and it is very frustrating to see them make choices that will not allow them opportunities later on in life. This is a dilemma that I face as a teacher, but it is certainly something that I will work on and try to change.