It highly depends on the design of existing application. If it had business logic, universal technological parts of code and application-specific code well isolated from UI, you could replace just the UI and the UI binding, otherwise it would be implementation from scratch, which is not such a bad thing: from my experience, really good applications were developed twice, and the first implementation served as a prototype useful for collecting experience and learning application field. Your second implementation can be done so it could have dual UI possible: both desktop and the Web.
I must say that porting the application to Web is much more difficult than in the opposite direction, due to really draconian limitation stemmed from limitations of HTTP, which is a stateless protocol. On of the fundamental concerns will be the state management used to preserve integrity of the application between field. Most likely, you will need to add JavaScript programming, likely with the use of Ajax, which looks totally foreign to your desktop prototype.
To get an idea, take a look:
If you choose to start with ASP.NET, for example, the problem of state management will look like this:
http://en.wikipedia.org/wiki/ASP.NET[
^],
http://msdn.microsoft.com/en-us/library/75x4ha6s.aspx[
^],
http://msdn.microsoft.com/en-us/library/z1hkazw7.aspx[
^];
See also:
http://en.wikipedia.org/wiki/JavaScript[
^],
http://en.wikipedia.org/wiki/Ajax_%28programming%29[
^].
—SA
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