If you're using broadband how are you disconnecting? Are you using the standby on the cable modem or actually powering it off (you should do the former by the way). Besides...why disconnect a 24/7 serbvice anyway...that's what you're paying for. No criticism - just don't understand?!
Incidentally, I've had Blueyonder broadband and Zone Alarm for ages and never had any conflict between the two.