Well, first thing to do is to make sure it's not the drivers.
Uninstall the current ATI drivers, then run Driver Sweeper and clean them out completely. After that install the latest 11.4 drivers.
You could try maybe an older driver revision.
Also have you OCed anything? If so, try running everything back at defaults (reset the BIOS to stock) and see what happens.
If that doesn't fix it, chances are the card needs to get RMAd, unfortunately. The PSU should be powerful enough, 5850s are only 150W cards.