Yesterday i got my new Sapphire 3850 512 and i installed it, got latest drivers and started testing it. For my big surprise i only had 4071 3dmarks (06). My rig is not extraordinary ( PentiumD 3.0 GHz, 2 GB memory) but i still think i'm too far from the scores they have in benchmarks (9000+).
then i turned to the PSU. I don't have a good brand 550W PSU http://myfreefilehosting.com/f/7dbc8fab19_0.52MB (here's a picture) and i'm afraid it doesn't deliver enough power to my HD. It says it has 24A/+12V rail and in the specification of the HD3850 it's stated that they recommend a 30A/12V rail.
The power supply is minimal, but it is running the card. I would replace it soon as you are pretty much maxing it out which will lead to failure sooner than later. It could actually damage your system when it dies also.
At any rate, a more likely cause for your scores is the old CPU. A common term is bottlenecking. To get the most from the newer vid cards, they really need to be pared with a modern processor such as a Core2Duo. While the Pentium is 3.0 ghz, the way it handles instructions makes it as slow as a low end Core Duo processor. In otherwords, your video card is outrunning the CPU, causing a bottle neck.
The Antec Earthwatts 430 is also 32 Amps so if its cheaper then get that (same compant so the quality should be the same).
I think your CPU is definatly to blame 3dmark 06 is very CPU intensive so that dosent help, you could try running it on the 05 but i dont know if you will have many to compare with. What monitor size and res are you using ?