It's very difficult to say what the issue since you are able to connect to the Slingbox remotely using a different computer. I recommend to check the anti virus settings to confirm this is not blocking the application. Do you have the same issue using Watch.slingbox.com?
I uninstalled slingmedia software and reinstalled, rebooted.
If you have the SlingPlayer installed in your Vista computer, I suggest to try the direct IP connection, it's necessary to get the WAN IP at the Slingbox location, you can use this 3rd party website, http://www.whatismyip.com/
Let us know how it works