I have had a similar issue with the 5850. After replacing my UD3 P55 motherboard (as I thought similar to above that hardware was an issue) the system was still unstable, with it sometimes not booting up and appearing to be in a holding pattern on standby. I then thought perhaps it was underpowered and replaced a 650 with a 720watt supply. Still no go then one day I inadvertently kicked the side of the machine and the screen flickered in that video card is playing up way. Turns out the card seats better in the second PCI port as there is some gear on the P55 UD3 that was holding the card up at one end by the smallest fraction of a mm.
Great machine but can be temperamental, this process took 5 weeks to sort out.