You could try looking at the logs (/Applications/Utilities/Console.app or something).
In the Mac's terminal, try:
ifconfig -a
If en0 isn't getting all of the proper entries filled (IP address, subnet mask, etc.) then there is an issue.
Then:
netstat -rn
There should be a default route type entry (could be gateway, router, default route, 0.0.0.0, or something else entirely I don't have a Mac on me). If it isn't getting that there's an issue with the DHCP.
Try an nslookup on the Mac, or try going to 64.233.161.99 in your browser.
If the nslookup doesn't work but going to the IP address does, it's definitely a DNS issue.