IIRC, that class of card can’t actually drive that many monitors. My 6870 can’t, so when I turn on my TV, I have to either move over to single-display mode or change the extended desktop setting from going between my 22" and my 17" to one going between the TV and my 17".
It may not be exactly the same config, but I had a hard time getting 3 moniutors to work on an ATI card recently. I could get any two displays to work, no matter the cable outputs, but the 3rd was always greyed out. It was only when I bought a display port to DVI ACTIVE adapter, that I got all 3 screens up and running.
DVI/HDMI share the same pipe, and that can only drive 2 monitors at once on the ATI cards. So that would be either DVI+DVI or DVI+HDMI but not DVI+DVI+HDMI. If you are wanting a third monitor you will need to start using the display/mini display ports on the card.
As someone stated you will need to use an active cable, and the one I bought the other year was about $30.
Also Armando your 6870 will do triple monitors if you have display ports on the card. Used my 6870 for quite some time in a triple monitor setup without an issue.