Thanks for all the help, legume and mdmadph! The card is installed and I believe it is working well enough. Unlike my attempt to move to this card in July, the Linux distributions that I use are now able to make use of the card.
I have to admit that my results are spotty enough to make me wonder if I should have bothered upgrading the card, or if it was a mistake to move to ATI. My move was from a GeForce3 Ti 200 with 64 MB RAM to a Radeon 3650 with 512 MB RAM.
One of my top-priority tasks is greatly improved: I can now browse directories of large photograph files quickly, with a greater capacity for storing thumbnails and thumbnails being generated more quickly. I take that to be a result of the increased video RAM.
However, my presently preferred Linux distribution, Mandriva 2009, stutters too much to be pleasant to use. It was working smoothyl under the geForce 3. I don't know what to think of that. I've used the backports feature to install the latest release of the Radeon drivers - version 8.10.
Things are fine under Kubuntu 8.10. Window movement had been slow under Kwin, but is perfectly responsive under Compiz. However, I was hoping to improve the performance in some minor areas of Compiz (i.e., some minor jerkiness in the rendering of some window transitions). That hasn't happened. The one real problem is that asking the system to shut down often stalls out at a black screen.
Should I attribute all this to the current software landscape and figure the bugs will all be worked out in time? Or should I return this graphics card again while I still can?