So basically I'd say it's your connector (dvi to VGA) is faulty if the screen isn't like that when your using your laptop I'd say that definitely the problem.
My advice if you bought I a few days ago go back and ask for a replacement. However before you do just try turning up the brightness on the screen that might be able to counteract your problem and assure that all plugs are properly plugged in.
I have the exact same problem, with the exact same monitor (DELL - E176FP [Connected to VGA]). I have determined my problem is to do with my Nvidia GeForce 210. What is even stranger is that I can drag an application from my SAMSUNG TV (connected to HDMI) to DELL monitor and the picture will be absolutely fine until it gets to about half way across, then it will turn dark. (XSplit, YouTube (flash objects)) and many other applications do this, except not Java written ones, e.g. Minecraft. This does not happen when the monitor is connected via my laptop's (Toshiba Satellite) VGA port. I do not think this is a compatibility issue, or a driver issue, I think it is problem the hardware connecting between my PC and monitor. However, as mentioned before, when I switch XSplit from one screen to another, the video feed goes darker, but it also goes darker on the fully working (or so it would seem) TV. Could you provide more information on your OS and hardware components? For example, Windows 7 Ultimate (Nvidia GeForce 210, 8 Core AMD processor, 16GB RAM)?