Question: Is there any system/compiler/SDK/IDE that provides an ability to develop desktop applications using JavaScript?

Answer: 
You can use **[node-webkit](https://github.com/rogerwang/node-webkit)**.

It uses webkit to render the webpage and execute the Javascript, and you will have access to all the Node.js javascript API (reading/writing files, …)
You might try [XUL](https://developer.mozilla.org/en/xulrunner) or maybe [Google V8](http://code.google.com/p/v8/).