I have the exact problem as you. I also have a ATI Radeon 4870, and I built a new gaming rig, but every time I boot up, the screen will go black and the fans go crazy and I will have to restart the computer three or four times before it stays stable until the next boot up.
I didn't know what was wrong with it, as I built it and there could be any number of problems, but since you have the same problem and graphics card, that seems to be the issue.
