and it doesn't like sharing it? Some motherboard resources like to grab IRQs like that IRQ Steering that Peter mentioned. Do you think that maybe the ATI card is grabbing an IRQ that another resource is also trying to grab? Then they don't like sharing it.
Try this, use the SiS card, disable the USB ports and extra serial port if you are not using them. Reset the plug and play settings for the motherboard, power down and then put the ATI card back in, see if that makes a difference.
See if there is a jumper or DIP switch on the ATI card that assigns the IRQ manually, then tell Plug and Play in BIOS to reserve that IRQ for a legacy device, and see if that works.