I see on the Nvidia website that they do have a new Linux driver for your card that you can download and install.
I assume you are running the newest bios and board chip-set updates. Linux is not plug n play, so you have probably set the bios to the "OS is not PNP compliant" option.
Do you have the flexibility of making this machine exclusively Linux, or do you have to keep XP installed because of other commitments?
It may be easier to diagnose the driver issue if the patient is of only one OS. You could try installing Linux with the old AGP card, and then rebooting with the new one.
Regardless, I have zero experience in the realm of dual booting on the same machine. What I do, since I have a LAN, is simply clone the Windows drive to a backup drive so that I can completely make the machine a clean Linux system.
That way, I am dealing only with Linux, and if it becomes unstable and I cannot fix the problem I can then simply use Norton Ghost to clone back my old OS and run with it.
I think your first step is to ensure that all of your firmware for your motherboard is current, and that your bios is set to disable the PNP OS, so that the MB can manage the hardware.
Once it is installed, then download and install the new Linux driver either from the manufacturer of the card or from Nvidia.
Also make certain that the bios settings for palette snooping, acceleration, timing, etc, are as specified in the owners manual or according to the specs on the manufacturer's web site.
XP may be compensating for something that Linux cannot recognize, and if your bios is not compatible with the new card, that may be triggering the problem under Linux.
I don't know if these ideas help you or not... I know that you are looking for one simple key, but since I do not run any dual boot systems, I am not familiar with the behavior of a system running two OS's at once.