Video Screen Capture in asp.net

If I understood correctly, you want to give the user the ability to capture video stream from the computer's screen and save on the client side. Is this correct?
If yes, this might be possible using Multimedia DirectShow objects, but you will need to either create a custom control or use a library that has such controls and install that control at the client side. This makes some restrictions since most internet browsers don't support ActiveX and COM objects. So this will work only on some versions of MS IE, but not other common browsers like Chrome or Firefox.

Alternatively, you can create a native.NET capture application and use click-once deployment. With this approach, you only send a link to your users and they can install from that link on their machines, and capture videos directly from screen. The easiest way to create a .NET capture application is to use an sdk that has .NET multimedia controls such as LeadTools.