Ok, let me get this straight:
Are you having trouble with DNS lookups, pinging, or both?
I'll assume: you have a Mac OS X machine that isn't networking correctly. On the same network, other computers running Win98/NT, Classic Mac OS, etc. work fine. Your internet access is via a computer attached to a modem or whatever that's running a simple proxy server.
On the OS X machine, Internet Explorer works, but Netscape and the Network Utility don't? (This part doesn't make sense; unless IE is getting web pages out of it's cache, if you can't use nslookup to find an address, neither can IE.)
Here's some advice:
Is your OS X machine getting a good IP address? That makes all the difference; a bad IP would prevent internet access, DNS lookups, etc. You shouldn't be able to ping outside of your local network (from any computer) if you're running a simple proxy server (I assume you're firewall is not acting as a NAT or router..).
Check and see what your other computers' IP addresses are, and manually assign a similar one to your OS X machine. Try pinging one of the other computers. If that works, then you just need to go into your web browser (which ever one you want to use) and set the proxy server addresses.
