Monitor's DVI connection died, VGA shows wrong resolution

I have a three-year-old Dell Dimension that came with a 22-inch E228WFP widescreen monitor connected to an nVidia GeForce 7900 GS video card. The monitor's native resolution is 1680 x 1050 and, until recently, everything was working fine. Then I started having a problem where, once the system got past the BIOS check, I would lose video completely. I could hear Windows starting up but I couldn't see anything. I took the computer into the shop to have it checked because I thought something was wrong with the video card. But according to their tests, everything was fine with the unit itself. This led me to conclude that there was a problem with either the monitor's DVI port or the cable.

I had been using the monitor's VGA port to connect my XBOX 360 so I knew that one still worked. When I connected the VGA cable to the monitor and connected it to the video card with a VGA to DVI converter, I finally got my video back but the resolution was all wrong. My monitor's native resolution is no longer available to me and the only listing in Device Manager is  "Generic PnP Monitor". I tried reinstalling the drivers for the monitor and video card but, even after that, I cannot choose 1680 x 1050.

Short of trying the "scorched earth" method, or replacing the monitor, does anyone have any ideas about how I can fix this?