There is a lot going on in that class. If you could narrow it down where we specifically need to look, that would be beneficial. Also, having a class named "Window" _could_ get hairy because of the reserved word "window". You may want be a little bit more specific: var PSWindow = new Class(...), or something like that.
With that said, chrome does not appear to have an issue with makeDraggable....
http://jsfiddle.net/CYgdx/ You may strip a bunch of the code out and slowly bring pieces back so you can see what's breaking the drag functionality.
Happy coding,
~Philip