Your graphics card should support being able to drive both a VGA and a DVI monitor at the same time.
ATI have a (slightly rubbish) guide on the basic steps to get it to work with the two monitors ATI Multimonitor Guide. Basically the show you how to run their setup wizard.
In the ATI Catalyst Control Centre you should see something similar to this, though I've no idea how old this image is what you are looking for should have a similar name:
Basically if your second monitor is being detected then you can enable it.
If on the other hand the monitor is not able to be detected you may need to check your connectors and cables to make sure they are all well seated. Possibly try booting the machine with only the VGA monitor connected to see if it works at all.
-=EDIT=-
Having re-read your question I think I understand your problem a little better. You are using the VGA output on your graphics card, and using the analogue output from the DVI port via a DVI-VGA adapter.
I'm still a little surprised that this did not work but it is entirely possible that the graphics card only has one set of hardware for converting the digital video signal to analogue VGA and so will only work with one VGA monitor at a time. This would mean you can use either the VGA or the DVI-VGA but not both.
I have a graphics card here that has two DVI ports, but only one of them will accept a DVI-VGA converter, the holes for VGA are missing so the connector cannot be plugged in so I guess this card would have the same problem you are experiencing, only one analogue monitor output.
Another thing to check though is if your graphics card has a DisplayPort output. If so you can get adapters to convert that to a VGA output. I have just recently had reason to buy a Displayport to VGA adapter which worked a charm for driving an old VGA monitor and it was cheap at £5 all in.
It seems that digital DVI to VGA converters are expensive (£100+) while digital Displayport to VGA converters are much cheaper at <£20.
Best Answer
Sorry, that graphics card only supports 2 simultaneous monitors.
Edit: If you're willing to spend some money, you could go for something like a Matrox display splitter (http://www.matrox.com/graphics/en/products/gxm/dh2go/digital_se/), but for that price you may as well just buy a new graphics card that supports triple monitors. (random example) There doesn't seem to be a software fix to this problem, it's just a limitation of the availible hardware.