|You might need to provide a link to an AGP version of the card. Your Dell 4600 has only an AGP8x slot and the ATI 3560 card reviews I've read all list it as PCIe2. Not compatible with your system.|
The highest spec ATI card with AGP interface I found was a Gigabyte ATI Raedon HD4650 which was available in either PCIe or AGP versions. I have the AGP version running in a P4 system. It has a relatively low power requirement but even at that your 250W Dell powersupply might not be up to the task.
Goin' Fishin' (Some day)