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Web technologies are evolving day-by-day and i am not quite up-to-date with the evolution.
However, I am pretty certain that you would need some sort of server-side processing. From the way you have framed the question, it seems to me, that you are not quite clear about the request-response model of http protocol on which the web works.
Connecting to sql server from javaScript, while might be possible (I am not sure), it is not a very good idea from security perspective, i guess.
And where would you put all your business logic?
Calling asp.net a front-end would be incorrect. It is a server side technology.
You can have all your front-end in HTML5, CSS and Javascript and write a server-side code in WebAPI.
You may wish to look into serverless architecture (I still not have looked into!)