You need to provide a little more info about this issue.
– Do you have free leases to allocate in the scope this specific client is in? (Check event log on the server to see if there is any messages related)
– Do you have some kind of MAC address filtering in place (DHCP Sever Callout DLL)? Since Windows Server 2003 in possible to install a DLL to filter DHCP requests based on MAC address.
– From my experience, it is also possible that an old, corrupted NIC driver can lead to this: a client unable to be delivered an IP address. Check if your NIC drivers are latest version available.
Hope this helps to find whats happening.