I have a ECS GEFORCE6100SM-M2 /AMD Sempron 3000+ that I was able to get working. Here's what I did
1) Setup a single SATA with no RAID (the MB uses NVIDIA Geforce6100 chipset for storage).
2) Installed an Intel Pro/1000 NIC (the onboard is not supported)
3) Installed ESX
4) On the first reboot, I selected the Service Console only (troubleshooting mode) boot option.
5) Let the host boot up and logged in.
6) Edited the file /etc/vmware/pciid/sata_nv.xml - change the last entry to use a device ID of 03f6 (and I updated the device name to MCP61 SATA Controller). I was able to determine the device ID by running lspci (since your MB has the nVidia nforce 560 chipset (yes/no?) you can run lspci | grep "nVidia" and you should see an IDE Nvidia controller that is an unknown device - make a note of the device id and you'll update sata_nv.xml to use that device id).
7) After saving the file, I ran esxcfg-pciid
8) Rebooted and the controller came up fine.
I did have to re-format the default vmfs partition with vmkfstools -C vmfs vmhba32:0:0:x, as the VI client did not see any free space on the drive. In hindsight I would not create a VMFS partition during the install next time I do this.
The PC has been running an x64 Windows guest for the last few days without any issues.