My Rode NT1-A mic is connected through a phantom power source and into a USB adaptor (this one - http://www.parts-people.com/index.php?action=item&id=5048) in my windows machine. When I use the sound recorder, I can hear myself testing it, but there's also a lot of buzzing. How can I fix this?

SOURCE: NT1A no signal in sequencer

try cleaning your plugs before inserting them into the machine. a dry clothe will do nicely. polishing the plug heads in a twisting motion.

SOURCE: Rode NT2 got Phantom!

Well... Rode NT2's are condenser mic's that require phantom power to work. So the phantom switch should be on. When you turn phantom power on you usually hear a bump sound (through the amplifier). In this case, nothing is broken.
Your picture is of a Rode Videomic (not an NT2) which is a stereo mic for video cameras. If you had some kind of stereo mini to (single) XLR adaptor, and put phantom power through it, the mic would probably be damaged. But maybe not... just try again without phantom power to see. a stereo mic won't work very well with the Mbox Mini because it only has one mic preamp. 

SOURCE: When I switch on my Rode NT1 - A mic - it is OK

I had the same issue. The sound would fade and then go dead.. The preamp in the device I was using wasn't strong enough and also the phantom power seemed too low to sustain the microphone. After adding a TUBEPre by PreSonus, all of the issues went away and I was shocked to hear how good this microphone really is. Was the issue low phantom voltage/? or a lousy preamp? All I know is , after adding a preamp all of the problems went away.This has to be the best microphone I have tried in this price range.