It looks like the problems with my Sapphire x1950 Pro are hardware related.
After rolling back the Catalyst version I was able to avoid the infinite loop issue, but the card itself is still displaying garbage all over the screen.
I went through AMD’s list of things to try, including sticking the card in another system, and it just seems to be the card itself.
I summarized this all in my ticket for Sapphire’s tech support. I guess it was convincing because they asked me to send the part number, serial number, and my receipt to an email address they provided, and they would issue an RMA number.
Part number and serial number are easy. I had those to hand already. But a receipt? I bought the card from ZipZoomFly.com, so I have an electronic receipt, so I am covered. Or I hope I am. I just wonder what I would do if I bought the card retail.