Hi,
You should use a dummy plug for the card whose don't have the monitor plugged. You don't have to have crossfire and I recomend to set the 4870 in the primary PCIe slot which you will use as primary.

The dummy plug simulate that there is a monitor plugged and you can use the 2nd card.

Here you have a link to make a dummy plug. You only need a DVI-VGA adaptor(which comes with every card) and some resistors.

http://www.geeks3d.com/20091230/vga-hack-how-to-make-a-vga-dummy-plug/

I hope it will help you. I have a 5850 in the primary slot and a 5770 with the dummy plug mining and it works for me perfect.