A quick way to solve this would be to statically assign some IP address to the laptop in the network settings - say .61
Reboot the laptop and then revert to dynamic assignment of the IP address using DHCP. The laptop should then send its DHCP request for .61 which the DHCP will likely honour.
Have you tried disconnecting the laptop from the network and pinging .60 to see if there is actually a machine with that IP address?