I'm guessing it's actually a mini-DisplayPort to VGA adapter you're using. Is it a 3rd-party item or genuine Apple? Either way it's quite common for these to be recognised by the host Mac and yet not output anything to the display. The reason for this is quite simple, mini-DisplayPort to DisplayPort/DVI-D/HDMI connections are digital and pass straight through to the connected display, the only difference between them is the form factor of the connector. Mini-DisplayPort to VGA adapters have a digital to analogue converter in the main body, and while the host Mac may be able to communicate with the DAC (as it would if connected to a digital display) it will be unaware of any faults downstream of the DAC. If there is an issue with the DAC (or the post-DAC analogue section) the result is frequently that the Mac thinks a display is connected, and will show mirroring and extended desktop options in Display Preferences and yet output nothing to the display.
Genuine Apple units are more reliable but more expensive. We've many (cheap) 3rd-party units around our campus, and we've had many fail after a few months, giving the same symptoms as you describe. Assuming you've checked the VGA cable is securely connected the other tests you can try are as follows...
Hook the display up to a Windows laptop if you can. Even relatively modern ones have a VGA connection. This will let you test the cable and display function.
If they both check out then you need to either try the adapter on a different Mac, or create an OS X installation on an external disk to make sure it's not your OS X install that's having issues. Having said that, it sounds like your Mac is correctly identifying and communicating with the adapter as you've already stated it thinks a monitor is connected.
A quick look for your model didn't bring up any obvious results but many Samsung's have a DVI connection. If yours does, get a mini-DisplayPort to DVI adapter as they're far more reliable.