To find manually-set DNS addresses in Windows ME, go to the Control Panel > Network > TCP/IP > Properties > DNS Configuration, and look in the DNS Server Search Order box. If it's empty or it says DNS is disabled, I don't know what to do from there. I'd say bitch to the cable company that yes, you do need them, and they should damn well give them to you because DNS servers aren't a big secret on any other provider. If they still won't give them to you, try entering 220.127.116.11 for the first and 18.104.22.168 for the second (I ripped these off from some random ISP, I'm not sure if they'll work for you, but if you run out of options, it's worth a shot).
(Incidentally, a DNS is a server that takes the URLs you type in (http://www.i-mockery.com
), looks on a gigantic table, and turns them into IP addresses (22.214.171.124).)