Which aspect of Windows do you want to simulate. Do you want to create an on-line "desktop" that looks like Windows 2003? In that case, check out whether you can customize one of the already existing Web Desktop projects like eyeOS. See the Wikipedia article on Web desktops for a list of projects.
It's going to take way more than basic HTML skills to work on a On-line desktop, so you really want to look at existing solutions unless you want to learn advanced Javascript, CSS and server-side programming from scratch.
To actually run Windows 2003 applications through an on-line interface is possible using the Remote Desktop Protocol and an appropriately configured Windows server (See the Link in Carlos's answer for a way to start a RDP session from a web browser window). However, this can't be done for free and is not unrestricted - you need to purchase the Windows OS, and user licenses for people to log on to the system.
Opening such a Terminal Server to the public is, as far as I know, forbidden my Windows 2003's license terms, extremely dangerous because of the risk of people infecting your system, and overall not worth pursuing IMO. You could do something like this with Linux because there are no license terms, but it's not a trivial matter and it's not going to run most Windows 2003 software.