Thought I'd join in this conversation as I have a system with hardware that is almost identical to that of OP's. I have a HP computer which uses the Asterope2 motherboard. The Asterope2 is based on an ATI chipset and incorporates the ATI Radeon Xpress 200 series onboard video. I also have a Sapphire HD4350 video card which I used on the HP for a while.
I didn't have any problem getting the HD4350 to work on the Asterope2. I just plugged it into the one and only PCI-E slot, went into BIOS and set "Primary Video Adapter" to PCI-E. It worked the first time. Then I updated the video driver to the latest Catalyst driver from AMD's website.
FWIW the HP also has 3GB of ram (only 2 slots) and an extremely cheap (I would have got my money's worth if it lasted just 6 months) 450W PSU. Thought the PSU would conk out after a few months. But surprise...it's still going strong after almost a year and the computer is on almost 24/7.