Can’t Connect To My Other Computer Through Remote Desktop. Please Help.?

Hello. Please help.
I can’t connect to my other computer through the Remote Desktop.
When I type my other computer’s full name (example: enriquepc1) or when I type the other computer’s IP address as suggested by the Help button (example: 192.253.7.100 found in my Local Area Connection) it still doesn’t work.
Both computers are setup to allow the remote connection.
Am I using the wrong “IP address”?
Maybe I should use the “static” IP address? if so, where do I find it?
I heard about using the computer’s DOMAIN NAME or “dns” I guess, where and how do I get this dns?
Is it provided by my internet provider? Or do I request it?
My internet provider is COX.net
Does this mean I should type (for example) enriquepc1.cox.net? I did and it still didn’t work.
I don’t know what else to do.
Would you help me?
The computer I wanna access to is Windows XP Media Center Edition. The one I open remote desktop connection is Windows Vista Home Premium.
Thanks,
Enrique.