There is nothing about .NET that requires you to pay.
Often, you will hear that it is not free, but this is referring to the GNU concept of “Free” as in “freedom”, not free as in price (or, in their words, .net is free as in beer but not free as in freedom).
You can use your student license to create .net applications. You can also download VS 2008 Express Edition, which is fully functional to develop.
Alternatively, you can develop in .NET using non-Microsoft products. Mono includes a completely separate, free runtime. There are even free IDEs available, such as SharpDevelop.
— EDIT —-
Yes. You can use .NET to develop and deploy a website, an application, or anything else. There is nothing in the technology itself that requires payment. The only thing that requires payment is certain tools (such as Visual Studio Professional Edition or the Visual Studio Team Editions). There are lots of ways to develop with .NET for free.
For free ASP.NET development, you have two options. The first is to use the Mono Project’s ASP.NET Implementation to run your site. This is completely free, and handles asp.net sites.
However, if you are paying for hosting, your host is paying the licensing fees for Microsoft IIS and the hosting of asp.net sites. The cost to you is included as part of the hosting.