I'm going to assume that C:\images\logo.gif is the path on the server, and not the path on the client.
The src attribute is interpreted by the html client (i.e. Internet Explorer). The client can't see anything outside of your web directory. In fact, the client can only see things inside your web directory if you've provided permission for them to do so. Thus, this isn't an ASP.NET issue, but an issue of how web clients have access to web servers... which is designed this way for security.
In order for your application to use these images, you've got a couple of options that immediately spring to mind - neither of which is ideal:
The ASP.NET code (in the codebehind) is going to need to go and grab the file, and serve it out in the html stream that is being served to the client, which is more a complex task than I suspect you are willing to embark on.
The ASP.NET code (using System.IO) is going to need to go and grab the file from it's home location in C:\images\logo.gif and copy it to a location that is accessible to the client - you could create a temporary directory, copy your image to it, serve it out, delete it, delete the directory.
Both of these are certainly hacks that should be avoided if possible, but if you're adamant that this is what you want to do, this will allow you to do it via your ASP.NET app.
The most ideal solution is to add C:\Images as a virtual directory to your document root, i.e. /ImageCentral - this way you can have images that are central to multiple websites stored in this directory, it can then be referenced by clients for any of the websites just by adding virtual directories to each of them pointing at the central images folder. As DaveSwersky points out, don't make any directories containing sensitive information virtual directories, the minute you add a virtual directory to an externally visible website, you're giving people free reign to any of the information in it.
Good luck