I have had a perfectly working configuration involving only one monitor for some time now, like this:

GeForce FX5700 (has VGA output and DVI output)
ViewSonic VG800 (18" LCD) connected to CRT output

I'd give more details but that has always worked. It still does. I decided to experiment with attaching a second monitor using the DVI-VGA adapter that came with my card. That monitor is an HP Ergo Ultra VGA 15 inch CRT. It works fine as well, except that it produces no red. Upon switching the way the two monitors were connected (and switching around the appropriate things in xorg.conf), my VG800 produced no red, and the little old montior was perfect.

So...the monitors are definitely fine. I don't know if a problem like this is likely (or possible) to occur because of the DVI-VGA adapter. I've included xorg.conf but I don't know what good it could do.

xorg.conf:
-----------------
Section "ServerLayout"
Identifier "Default Layout"
Screen 0 "Screen0"
Screen 1 "Screen1" rightOf "Screen0"
InputDevice "Mouse0" "CorePointer"
InputDevice "Keyboard0" "CoreKeyboard"
EndSection

Section "Files"
RgbPath "/usr/X11R6/lib/X11/rgb"
FontPath "unix/:7100"
EndSection

Section "Module"
Load "dbe"
Load "extmod"
Load "fbdevhw"
Load "glx"
Load "record"
Load "freetype"
Load "type1"
EndSection

Section "InputDevice"

# Specify which keyboard LEDs can be user-controlled (eg, with xset(1))
# Option "Xleds" "1 2 3"
# To disable the XKEYBOARD extension, uncomment XkbDisable.
# Option "XkbDisable"
# To customise the XKB settings to suit your keyboard, modify the
# lines below (which are the defaults). For example, for a non-U.S.
# keyboard, you will probably want to use:
# Option "XkbModel" "pc102"
# If you have a US Microsoft Natural keyboard, you can use:
# Option "XkbModel" "microsoft"
#
# Then to change the language, change the Layout setting.
# For example, a german layout can be obtained with:
# Option "XkbLayout" "de"
# or:
# Option "XkbLayout" "de"
# Option "XkbVariant" "nodeadkeys"
#
# If you'd like to switch the positions of your capslock and
# control keys, use:
# Option "XkbOptions" "ctrl:swapcaps"
# Or if you just want both to be control, use:
# Option "XkbOptions" "ctrl:nocaps"
#
Identifier "Keyboard0"
Driver "kbd"
Option "XkbModel" "pc105"
Option "XkbLayout" "us"
EndSection

Section "InputDevice"
Identifier "Mouse0"
Driver "mouse"
Option "Protocol" "IMPS/2"
Option "Device" "/dev/input/mice"
Option "ZAxisMapping" "4 5"
Option "Emulate3Buttons" "yes"
EndSection

Section "Monitor"
Identifier "Monitor0"
VendorName "Monitor Vendor"
ModelName "ViewSonic VG800"
DisplaySize 360 290
HorizSync 30.0 - 82.0
VertRefresh 50.0 - 75.0
Option "dpms"
EndSection

Section "Monitor"
Identifier "Monitor1"
VendorName "Monitor Vendor"
ModelName "HP Ergo Ultra VGA 15in"
DisplaySize 277 208
HorizSync 48.4 - 56.4
VertRefresh 70.0 - 75.0
Option "dpms"
EndSection

Section "Device"
Identifier "Videocard0"
Driver "nvidia"
VendorName "Videocard vendor"
BoardName "NVIDIA GeForce FX (generic)"
BusId "PCI:1:0:0"
Screen 0
EndSection

Section "Device"
Identifier "Videocard1"
Driver "nvidia"
VendorName "Videocard vendor"
BoardName "NVIDIA GeForce FX (generic)"
BusId "PCI:1:0:0"
Screen 1
EndSection

Section "Screen"
Identifier "Screen0"
Device "Videocard0"
Monitor "Monitor0"
DefaultDepth 24
SubSection "Display"
Viewport 0 0
Depth 16
Modes "800x600" "640x480"
EndSubSection
SubSection "Display"
Viewport 0 0
Depth 24
Modes "1280x1024" "1280x960" "1152x864" "1024x768" "800x600" "640x480"
EndSubSection
EndSection

Section "Screen"
Identifier "Screen1"
Device "Videocard1"
Monitor "Monitor1"
DefaultDepth 24
SubSection "Display"
Viewport 0 0
Depth 16
Modes "800x600" "640x480"
EndSubSection
SubSection "Display"
Viewport 0 0
Depth 24
Modes "1024x768" "800x600" "640x480"
EndSubSection
EndSection

Section "DRI"
Group 0
Mode 0666
EndSection