>When you are referring to "web project structure" I think you mean all the pages (.aspx), classes, images, etc. If so this is easy.
>I also found that I have a folder
>...\My Documents\Visual Studio Projects\MyApsnetProject.

Yes, those are the two related directory structures for a Web application.

>This folder has only one file: MyApsnetProject.sln. It looks like I just need to copy this file to the \Visual Studio 2005 Projects\MyAspnetProject folder on the new computer. Maybe it will work.
>
>One other thing I am trying to do is to "move" only one project from the VS.NET 2003 solution. And I am sure that when I try to use the .sln on the VS.NET 2005, it will start "complaining" on missing files. Hopefully the choices presented by VS.2005 will be easy to follow.

Not really, that is why I mention that you might have to update the configuration file to adjust for the new paths. The .sln file is the one you may want to take a look into.

I also assume that the project virtual directory has been created. If you create it with the same name as the other PC, then you should be ok.