You should know either VB.NET or C# before you learn ASP.NET, because ASP.NET lets you build interactive Web pages that use VB.NET or C# to handle what the user types or clicks.
For VB.NET and C# you need a logical mind, attention to detail, and patience. It helps a lot to have Visual Studio at home so you don't have to do your homework in the lab. Pay attention when the instructor shows you how to step through a program.
It does help to know a programming language before you start a new one, just because you already know the basics, e.g., what is a variable, what is an array, what is a loop, how to debug. But everyone has to start somewhere.
I don't know anything about NIIT. They should tell you if they have any prerequisites before taking your money for a class.