Graphics card cannot see DisplayPort monitors

I have just bough two refurbished Dell E1909WDDc DisplayPort monitors. Whatever I connect them to the PC cannot see the monitors at all. I have an HD6850 and have tried a VTX HD7770, both of which have full-sized DP sockets, so no adapter has been necessary. I'm running Win 7 32-bit with all graphics drivers up-to-date
Am I doing something wrong, or should these 'just work' ?
I have tried:
1) booting up on VGA and connecting the DP monitor
2) disconnecting VGA after booting, with DP monitor connected
3) booting up with only DP monitor connected.

Under all circumstances the monitor just flashes full-screen, white-black-red-green-blue. Have I bought faulty monitors, or is there some secret driver/option/switch I need to change?

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