See if I have this right please

Copyrighted righted music means I can not use the music unless I get permission from the writter and his or her pubisher.
Now if the writter goes to the Creative Commons, he or she now gives permission to people to use their music for non-commercial/non-profit use as long as their still getting credit for their work.
Now my question is could I use there music on my public gamming server after the writter of the music has a license with the Creative Commons?
My server is a public gamming server where people come to play a game (Team Fortress 2) on the server we can talk with one another through our mics and play a war game. Now I want to put music on there that people can listen to and would like to listen too. Now remember there is no fee to play on my server nor do I collect any my from running this server.
We provide a non-profit gamming server for people for people to come and have fun and the Creative Commons licensed music will not be used for commercial use nor will we be using this as a way to make any profit from it's use and the writers name will not be altered in any ways so he or she will be reaconized for his or her works.