I have Comcast and have had the same IP for a couple years. Renewing doesn't change it, leaving the modem uplugged for a day doesn't change it either. In my case, if I wanted it changed Comcast would have to do it.
Usually, when a board bans an IP, it's not just your IP, it's the range your IP is in, so if your cable company gave you a new IP, you may still not be able to get in.