Try closing Flash Professional, and then debugging with Flash Builder. They both use the same mechanism to debug, so it's possible Flash Professional still has the socket open, so Flash Builder's debugger can't do what it needs to do.
I have the same problem: whatever I try, there is no connection possible between the debugger and my online flash site.
I have uninstalled/reinstalled flash players, I have no other programs running, I even switched off my firewall just to check.
In the case of Flash Professional, a connection is established between the Flash Player Debug version and the Flash Professional Debugger while running the swf (whether local or published on a web server). You right click on the Flash area in the browser and select remote debug.
In the case of Flex, a connection is established between the local swf that has just been built in debug mode (in bin-debug) and the Flex Builder Debugger (or Profiler).
If you want to run the Flex Debugger or the Flex Profiler, launch the application from Flex Builder in Debug mode or in Profiler mode respectively. Do not try to publish your swf on a web server, right click and select remote debug as you do in Flash Professional. It won't work.
I have also found I coult only make the Profiler work in IE, not in Firefox.
I'm on a mac and I've tried Firefox and Safari, both aren't able to establish a connection.
I even put a crossdomain.xml on my server to see if that helps, and I switched off all firewalls and everything.
I'm really pulling my hair out since there's so little documentation. It just doesn't work and that's it.
Strangely, I do get runtime error messages in a popup (even if I set 'allow debugging' to false in export settings :-)
At least that's something that helps.
To inspect variables I now use DeMonster debugger. This also lets you trace messages and doesn't require
the hassle of adobe's own debugger.
Indeed, you will always get runtime error messages in the Debug version of the Flash Player, even if you set 'allow debugging' to false in the export settings
Again, AFAIK, remote debugging is not possible with the Flex debugger, only with the Flash Professional debugger.
With the Flex Debugger, you debug locally, launching the app from Flex Builder which opens the browser and runs the local swf.
But I don't use Flex :-) It sounds a lot easier though.
Right now DeMonster debugger has helped me out since it works both locally and online. Just open a SWF no matter where it is, and you can access all its methods and properties!
The only thing it doesn't do is give runtime errors but this is the one thing that adobe's flash debug player does.