Analog signals are not '100% works or black screen' so interference can be introduced and displayed, whereas with digital it is '100% works or black screen'. This is why we can hear fuzz on AM/FM bands and we hear music or nothing from Satellite radio.
To understand what's going on, you need to understand what is going on with each of the pins on a DVI to VGA adapter.
First, the adapter that you have looks like it's in rough shape. That adapter is missing the pin that controls analog vsync (not the same as turning vsync on in a game). This is part of a standard DVI-A connection. This could be why your getting blurriness. Please see the links below for more info:
DVI
http://en.wikipedia.org/wiki/Dvi
VGA
http://en.wikipedia.org/wiki/VGA_connector
There could also be interference in the cheap adapter from metals used or bad ground etc.
You own a GTX 580. You need to treat it well and not connect junk connectors to it. Buy a DVI to VGA connector that's not faulty with missing pins.