it does happen to be also an ATI RageXL PCI card
That's the problem right there, it it was any other make of card than an ATI one it would work. What is happening is that that old card isn't using the same driver as the 4670, and while Windows 7 can use two cards from different manufacturer, if the cards are the same manufacturer they both need to use the same driver model (in your case the 4670 uses the WDDM 1.1 driver model, and that old RageXL isn't even on the map).
Same thing would probably happen if you tried it with a new Nvidia card, and a similarly aged Nvidia PCI card.
Not sure if it will work on not, but one thing you can try is to use the onboard video and your 4670 at the same time. From having a look here (scroll down to Video),
it should work. reason for saying it should work is that the onboard video isn't trying to use the same driver as the RageXL and the 4670.
For what its worth, the Sapphire Radeon 4670 card has a third HDMI output - do you think an HDMI -> DVI adapter would be able to drive a third monitor from the same card?
No it won't. While the card may have 3 outputs, you can only use two of them at a time as there is only 2 RAMDAC's on the card. That isn't to say that you can't hook up all 3 at once, and then enable the two you want to use from within Windows.