An aside, it's odd that G.D. won't give you the IP addresses, they're usually very cooperative. This raises a suspicion that the IP addresses for those name servers may be dynamic (not likely, but still . . . )
Any domain name registrar, including godaddy.com, will have a whois link (well, all the ones I've seen . . . ) Follow the link, enter the name server domain. It should list the IP address as part of the whois info.
Another way, in Windows:
Type cmd or command in the run text box, press enter (or OK button)
A number of things here will reveal an ip. type ping [servername]
It will return 4 pings, "pinging [IP address] with 32 bytes of data"
A more complex one is tracert (trace route)
which traces the route from your computer to the host, but it also says "tracing route to domainname [IP address]"
If you have linux, you can just do whois from the command line