A list of IP addresses on the LAN will be of limited help, as the issue is there are two machines trying to use the same IP.
I would suggest that you attempt to find the MAC addresses of the two machines that are clashing.
What device logged the IP address conflict? Was it a server, router etc? Some platforms (Solaris, BSD) will log the MAC address of the offending host along with the error message. If the IP in question is within one of your DHCP pools, it's also worth checking your DHCP server's logs for the MAC address it's attempting to assign that IP to.
Failing that, I would recommend logging on to the default router of the subnet that this problem is occurring on, and monitoring the ARP table. There should be one IP address that flips between multiple MAC addresses; again, those two MAC addresses represent the devices you are interested in.
Once you have the MAC addresses of the two devices, you should be able to tie them to specific switch ports. This question provides more information on how to do that. You can also use an OUI lookup tool to help identify the manufacturer of each device.