Can i have my website files on one server, but run them through another using IIS?

You can do this, but it’s going to lag considerably. I would highly recommend keeping your web server and files local to one another. Or at least keep the data on the faster server other wise you are going to run into a lot of server side lag.

What exactly do you mean by “files for my website”? Data? Code? Both?

No the files need to be hosted on the same server. Fortunately, IIS isn’t that hard to setup. Unless I am misunderstanding the question but as someone who hosts websites on the side it’s not possible to do what you want.

This is possible, but I would recommend only hosting static files. For example, all code, databases, and HTML templates would be hosted on the fast server, and the CSS files, videos, file downloads, images, etc. would be hosted on the server with lots of HD space. Instead of setting up the first server to forward requests of static content to the second server, you should set up a completely separate Windows Server instance (or lighttpd server for a possible optimization for static content) and host it at static.example.com. All links to static content on the root domain should point to the second server’s subdomain.

I’m going to have to agree with @Vortico and @jasonwhite – you should really be putting the data on your faster server. In the web hosting game, disk speed is really important. You don’t want your website visitors to be impeded by a slow disk that’s serving up your documents at a glacial pace. The slower computer should be the one running the IIS server – chances are its NIC can handle the bandwidth requirements. The best solution, though, is to have the IIS server and the data/files on the same computer.