The network administrator should have tools to detect the problem but
you can try this method (i never use it when i have an ip conflict)
First : launch "ifconfig" and see your ip address/netmask. I assume that
is 192.168.1.2 with a netmask 255.255.255.0
Second : launch "nmap 192.168.1.0-255" (adapt according your ip and
netmask). I take some minutes (less than 5 in most of cases). This
method works if the machine on the network don't block each reply from
nmap, but i think it's so if your network adminstrator did his job ;)
Now you will see each ip used on your network.
Third : Switch to a static address that has not been listed by nmap and
see if you have problem. If you have one, try another till you find
temporary a ip address which is not used
Fourth : in root, do "arp 192.168.1.2"(your first ip address which gives
the conflict). Normally, it will show you its mac address. With this
one, you can see your network administrator.
I repeat that i never used this method with an ip conflict. I may not
work but if it works, i'm glad to know it.