Can you ping the computer's loopback address (127.0.0.1)? Can you ping the computer's IP address from that same computer -- in this case, 169.254.x.x? If you can't, you have issues with the TCP/IP configuration on that computer.
When you connected the other laptop, did you use the same Ethernet cable and wall connector (if there is one)?
When you open the Network and Sharing Center, does the connection type show as Home, Work or Public? Change it to Work if it's not set that way now.
Is the netlogin service enabled or disabled? Enable it if it is disabled, and make sure it's set to Automatic.
If those don't work, you could try this:
Change the network type to workgroup, do an ipconfig /release, and disconnect it from the network.
Remove the computer from the Computers OU.
Remove the computer from DNS if it's there. Remove the DHCP lease if it's still there.
Rename the PC, reboot it.
Plug it back into the network, add the computer to the domain, reboot it again.