That adapter won't work. VGA is an analog connection while DVI is digital.
This is not correct... exactly.
DVI is DVI and comes in many flavors. DVI-A is 100% analog and is the equivalent to VGA. You never see DVI-A connections because they just use VGA. There is also DVI-D - which is 100% digital. This is similar to HDMI, except no audio and a few other minor differences. The most common DVI connection is DVI-I which combines DVI-A and DVI-D.
If your Mitsubishi display has a DVI connection, then you just need to find out if the connection is DVI-I. If it is, then you use the adapter linked to in the first response above and that should be it. Check the resolutions that your display supports on the input side and match the output of your PC to that.
FYI... Many video cards these days will support component video output at 1080i and 720p resolutions. This is nice if you want to use more standard cabling and connections, but it may not be as good as a VGA connection.