I don't think Asp.Net is really based on a Design Pattern. It's just a Framework developed with a similar concept to the Windows Forms.
If you want to use a pattern to develop a Web Site with .Net Framework, I suggest to have a look to Asp.Mvc. It's another technology from Microsoft based on the MVC pattern.
At first point, I have partially misunderstood the question. If you are trying to understand the pattern eventually behind Asp.Net to convert it into a MVC pattern, well, there is no pattern as I said before.
Asp.Net it is totally based on the postback concept. Basically, every time an event (like a click on a button) is fired, the Asp.Net engine execute a post request to the same page, so it can call the method attached to the event.
So, if you want to convert the old project using an MVC pattern, I think you will spend most of your time converting the events into manual post requests.
Anyway, when you are facing a conversion from a technology to another it's better to understand what happens behind the scenes, instead just converting literally the old code into the new one.