They don't ban "your" ip address, they ban your ps3 account, it's Sony they can do that, nothing to do with ip addresses. Activision ban you from your connection through your "routers" ip address, set by your provider. So your router gets banned from activisions servers, along with the account. So it depends whether you were banned by Sony or whether you were banned on a game like call of duty.
PS, your ps3 gets a new ip everytime it connects, unless you've manually set an ip in your connection settings, which then gives it a static ip.