You don't have a static ip, Cute.
Anyays if you are doing the "Go Offline" option on the launcher, it is because we have banned the name "player" which is default for playing offline with the official launcher. Now that your using anjo caido's launcher and that isn't working it could be something with your minecraft.jar
Next time you launch it try and update your .jar and see if that helps, if it doesn't work uninstall java and re-install java.
These are only suggestions, as I haven't actually seen anyone else with this problem then BlazingBird who is a staff member and his problem got fixed by not playing for a month or so somehow?