Is your problem now resolved?
If not then here's some info.
First, you do NOT have to have both the DVI and VGA cables connected at the same time. It does not hurt, but your monitor will only use the input from one or the other, and ignore the one not being used at the time. It does not hurt to have both connected. I have a couple multi-input LCD monitors, and I have both inputs connected at the same time. But my inputs are coming from different computers, so I use the monitors own input switch to flip back and forth between the different computers. (I do it that way because this current KVM, a Keyboard, Video, Mouse switch, does not switch DVI inputs).
The resolution does not have to be identical between the inputs, either. However, it only makes sense to supply a resolution to the monitor that is the screen's native resolution. In my case it is 1920x1200, and my other large monitor is 1680x1050, just like yours.
Now, if you are getting an "Input not Supported" message (on the monitor) that is either; telling you that you are not connected to the correct input (that's possible is you have multiple inputs on the monitor - however it sounds like you are using both of a probable two, anyway). Or, it is telling you that the resolution signal you are sending to your monitor is not the correct range pixel-wise (like 1680x1050) or else, the refresh rate is too slow, or more likely, too fast, for the monitor's circuits. Try to see if you can set your refresh rate to 60Hz. 60Hz is the most supported refresh rate for LCD monitors. While 60Hz is not the best for tube-type monitors, since it can cause screen flicker (I can see it, some people can't) or even headaches and eyestrain. However, in LCD monitors, because of their inherent slowness of pixel change, you will not notice a screen flicker at 60Hz.
Since it sounds like you have selected the correct HxV (1680x1050) "size" I would guess that you may have the refresh rate higher than 60Hz. Not every LCD monitor is going to support 85 or 120Hz. Try 60Hz and see if that works.
Get back to us.