How do you set up 2 monitors?

I was previously using a 30" samsung widescreen monitor.
Over the summer it decided to die...
I replaced it with two Samsung 27" (SyncMasterP2770) monitors.

I'm running Win7 (Home Premium) 64-bit.

Either monitor on its own runs fine.
I'm using a GTX 570, with an HDMI port and two DVI ports.

When I connect both monitors (either HDMI/DVI or 2x DVI), one is on and the other is off.
Either monitor, in either DVI port or the HDMI port works fine, when its the only monitor connected.

There is an option for Extend Display, or something very similar to that wording.
When I choose that, the "off" monitor flickers a little and then remains black (off), except the power lights are on along the bottom... so I know the monitor is not actually off.
If I choose to display the desktop on one monitor only, that monitor then wakes up, and the other one stops goes dark.
The Extend Display option will then make the original monitor flicker initially when that option is picked.
But only whatever monitor that was set for "Display Desktop on Monitor X only" displays anything.
I can bounce back and forth between which monitor has the desktop on it, without changing any of the plugs, by changing that setting.

Kind of stumped on getting both of them on, at the same time.
Any help would be appreciated.

When you're at the point where one is on and the other is 'dark' but on... have you then tried to reboot the
computer when it's in that state?

you can try plugging both monitors to different card, if you have one spare. It seems, that the problem might be with your 570 as is unable to run with both monitors on, probably HW fault.

Just tried rebooting, while the system was set to "extend displays" and one of the displays was dark and the other visible.

On boot up, the "visible" side is still visible and it is set to "show desktop on monitor x".
And the dark side monitor has the power icon flash, which shows it is in standby and awaiting a signal (the same as the main monitor, if I shut the PC down but don't power off the monitor).

I'll see if I have any older video cards around; I usually pass my stuff on to friends or relatives when I upgrade.
I suppose even a really old card that would not box well, could show if the card is the issue.

It could easily be the video card; anything I buy from my local store has a four year "instant product replacement" warranty.
If the card is defective, I'll get a brand new one at no cost, or the next card up if my card is not available.