Dual monitor help

I have 2 PC’s and 2 LCD’s. PC A has dual VGA outputs. PC B has a DVI and VGA output. Both monitors are Viewsonic VG930m’s that have both DVI and VGA inputs. I want to be able to use both PC’s (not simultaneously) with dual monitors. So, I have hooked up PC A to both LCD’s using VGA cables. Then I hooked up PC B’s DVI output to one LCD DVI input and PC B’s VGA output to the second LCD DVI input using an Analog DVI to VGA HD15 M/M Monitor Cable. The second monitor doesn’t show anything or doesn’t even recognize an input.

I know that both inputs on the LCD work because I have tried each input individually using DVI-to-DVI and VGA-to-VGA. Am I using the wrong cable? Is it possible to go from VGA to DVI?