To have FIFA 2004 recognize it I changed the name in the registry to Logitech DualAction USB, as suggested in another forum:
http://soccergaming.tv/showthread.p...;threadid=85861
To fix the right stick, after some browsing in the forums I found that I had to change the attributes of Axes 2 and 5 in the joystick registers, as follows:
#3983