What is the DisplayPort-to-DVI/HDMI/VGA adapter you are using?
I'm currently running Eyefinity with three Samsung 932BW+ monitors (CrossFired 5770)
Obviously, all of my monitors are the same. But, before I bought the Active DisplayPort-to-DVI connector (Accell), I had a passive DisplayPort-to-VGA connector... I had black screen problems with it, thus, the change to an active connector.
Also, I must ask: Are you really using "Eyefinity" or are you just trying to run 3 monitors in extended mode? I ask because the Eyefinity requirement is:
Can I support different resolutions?
All monitors running in a Display Group or cloned modes must be running with the same resolution. If monitors have different native resolutions, the highest common non-native resolution between the monitors will be used when creating Display Groups. Monitors running in extended desktop mode can have independent resolutions.
(AMD Eyefinity FAQs