I haven't used Linux on dialup at all, but I suspect that most of the important pieces should be the same as on cable/DSL.
I always try to troubleshoot stuff from the command line. Do an 'ifconfig -a' to see if you have an IP address from your ISP. You will probably see a couple of devices listed, not sure what names they'll be.
Assuming you have an IP address, since you're having name resolution problems I'd 'cat /etc/resolv.conf' to see if there's a nameserver specified (there should be). Try to 'ping <nameserverIP>' to see if you are able to reach the DNS. (Ex: ping 68.42.244.5 ) You may want to 'man ping' to see what the output should look like.
If you are able to ping the name server, then try doing a lookup for something like Google or Yahoo. I know it's deprecated, but nslookup should still function for you, I believe. Do an 'nslookup
www.yahoo.com' and it should report back the name or IP of the name server, then the IP address for the name you requested.
If it does return an IP, see if you can ping that IP successfully. If that works, then try pinging it by name. I'm pretty sure that if you can ping it by name, then you should be able to get there with your browser or other app.
If you can't ping your name server, it's likely that your routes may be messed up. Normally, dialing in again should set the routes properly for you, but if that doesn't work, you may want to reboot to clear the routing tables. (There's probably another way to do that without rebooting, but I'm not quite a pro.)
After rebooting, try dialing in again and see if you can connect with your browser. If not, check whether you can reach your DNS again. If you still can't reach it, or if you still can't ping sites by name, you may have problems at your ISP, though many of them seem to not know what to do if you're running anything other than Windoze.
Hope this helps at least a little. It's kind of a lot of things you might need to check, and I haven't hit all of them here.
-alan
