Since your PC is working before upgrade to the new graphic card,
Check if there a minimum power requirement for the graphic card.
I think some graphic card require power supply to be at least 480W.
Flash the motherboard BIOS to the latest if necessary.
Set AGP setting in BIOS as per Static recommendation.
Reset BIOS setting to default if necessary. Do not select "optimum". (Do not overclock)
Boot it with only your boot drive first. Disconnect the other 2 hard disks.
Check that your chipset and graphic card driver are not too old. Use 1 version before the latest if necessary.
Use a single stick of RAM if necessary (system usually don't auto reboot unless is hardware failure or going to fail. Most of the time is RAM). You might need to do a burn-in test.