I was helping a friend with a problem that sounded very similar to this. He could ping the nameserver but couldn't resolve any addresses, just as you described. We found your problem description here before we found our solution. I'll post it in case it helps you.
For us the problem was ipchains. Prior to the RH8 upgrade, he had selected IP firewalling with ipchains. RedHat 8 didn't upgrade that feature correctly. It preserved the ipchains settings in place which deny inbound UDP packets, but not the code in /etc/sysconfig/network-scripts/ifup-post which was adding a hole in the firewall for the nameservers listed in /etc/resolv.conf.
There are several ways to solve this. I couldn't find a GUI tool to modify ipchains (which I think may only be available during RH installation or disappeared in RH8) so I used the ipchains command line utilities. The HOWTO is at http://www.netfilter.org/ipchains/HOWTO.html
. You need to enable UDP Port 53 (DNS) packets to come into your machine, at least from your nameserver if not the whole Net.
As root, add a line like this to /etc/sysconfig/ipchains before the REJECT lines.
-A input -s 0.0.0.0/0.0.0.0 53:53 -d 0.0.0.0/0.0.0.0 1025:65535 -p 17 -j ACCEPT
and then run "/sbin/service ipchains start"
There may be a GUI-based solution we hadn't considered. But this got the job done for us.