Resolve hostname 2210-02-1006 and other issues

I'm running Windows XP SP3, high speed DSL through AT&T, PPPoE connection. I'm troubleshooting my Motorola (Netopia) 2210-02-1006 modem in addition to verifyng DHCP, DNS settings of the modem and the local area connection.

Question concerning 2210-02-1006 modem: having accessed 192.168.1.254, under the "Local Network" heading, should I have the box checked or unchecked for "LAN DHCP Server Enable"?

Next issue concerning 2210-02-1006, when I run full diagnostics, IP results in "Fail" . Then when I run a ping test, it says "cannot resolve hostname". Does this matter or will my connection improve if it is resolved?

Next, under "Local Network", after I've selected the "DHCP" link (the top of the list of links to the right of the main info), should the "LAN DHCP Server Enable" box be checked or unchecked"

Finally, my PC/s local area connection , under TCP/IP properties' General tab, after clicking on the "Advanced" button below "Obtain DNS server addresa automatically" , then clicking the "DNS" tab, should I have the box checked next to "Register this connections addresses in DNS"