I'm currently a ASP.NET developer, straight out of university.
My experience of ASP.NET comes solely from picking it up a year ago at an internship and using it and C# (with a bit of VB.NET for kicks) to build my final-year project (a search engine).
It's a world apart from classic ASP, but if you're capable of programming in an object-oriented language like Java and can get some practice with ASP.NET I'd be inclined to say that with a bit of practice you can land a decent job without much professional experience.
Build your own site using ASP.NET, and perhaps get yourself a bit of CMS experience with something like Umbraco. Once you're comfortable with it use that as your reference, state your past experience and I think you'll be just fine.