What do you get in the bluetooth prefs pane? Does it allow you to turn BT on there? Is your computer set to discoverable, or are you not able to access that setting because of the crossed out BT icon?
What Varmit said sounds like good advice, at least as something to try....
If you see the BT dongle in the system profiler, then apparently the system is willing to set it up / has a driver for it / etc....
As far as having a bad mouse...so your other dongle sees it, but refuses to pair it, or at least it refuses to work when you pair it. Hmmm...I guess it's a possibility. Can you try it on anyone's computer that you know has working internal BT? But it seems like an unlikely candidate for simplest explanation as long as you've got a crossed-out BT icon on your menu bar...you gotta get rid of that first.