Now I tried this with a bit older motherboard with Intel 915GM chipset and there are troubles. ATI X300 board work well, but Nvidia boards not - the device manager reports "The device cannot find any free Input/Output Range (I/O) resources to use. (Code 12).

This is really strange because there are no conflicting ports that these boards use.
If I try to assign resources manually, the following list of resources appears:

so the only problem seems to be with memory ranges:
00000000 - 0FFFFFFF (256 MB)
00000000 - 03FFFFFF (64 MB)
00000000 - 00FFFFFF (16 MB)
00000000 - 0001FFFF (128 KB)
The graphics board ic conncted correctly to the PCI Express Root Port:

the memory range assigned is: B0000000 - CFFFFFFF:

Windows XP on the same computer shows the same range for the PCI Express Root Port but also assigns correctly the four memory ranges for the graphics board:
B0000000 - BFFFFFFF (256 MB)
C0000000 - C3FFFFFF (64 MB)
C4000000 - C4FFFFFF (16 MB)
The fourth range (for 128 KB of RAM) is not present in Windows XP, but the same situation is for ATI X300SE so probably it is OK.
I tried to disable all integrated peripherals and left just the harddisk and the video card, and the conflict has not disappeared.
The on-board Intel graphics is always disabled.
I also tried both Windows 98 SE and Windows Me with the same result.
Of course, I can use ATI board and forget this problem but I like to see things working
Does anybody have any idea how to assign the right resoures or find any possible conflict? Is there any debug mode in which it would be possible to find the root cause?
Petr