Are these DVI monitors? or VGA?
DVI has several formats, One is all anaolg signals (DVI-A), the other is pure digital signals (DVI-D), and the last combines both (DVI-I). You cannoth use a dvi-d monitor of a dvi-a gpu and vise-versa. Dvi-i will work on either provided you use the correct cable (dvi-a/dvi-d/dvi-i)
Vga is all analog signals only so the problem is probably resolution or refresh rate. Try using the monitor that works and set the resolution to 800x600 @ 60hz refresh rate and then swap monitors and it should work since thats a standard svga resolution. Once you can see the screen you look up the native resolution of the monitor you're using and then set the resolution and refresh rate to that.