So, what is the server part of your game doing?
Is it more a scoring/leaderboard thingy, or does the server part creates game elements (information, maps, scorings, RNG, and so on) essential for the game?
Just installing a Stencyl-game on a server wouldn't work as the Stencyl-blocks are client-side only, there's no HTTP-Listener. Implementing such could be possible, but doesn't really make sense.
Dreamweaer is not really a tool to create a server part, it's a tool to create web pages (more ore less dynamic), but this pages need a web-server who hosts this.
Finally, the basic setup for a HTTP-Server as a game back-end typically looks like this:
1. Webserver (e.g. Apache)
2. Database server (e.g. MySQL)
3. Java / PHP / Grails / Ruby / JavaScript-Install...whatever
With the prefered language mentioned in 3. you develop your game back-end that relies on the database in 2. and serves it information through 1.
(We're using Java for all back-end related stuff in our games and services)
That's not really complicated, but if you have never done this, it's a tough job.