Is this a new subscription you are trying to set up? Or have you been using 360 for some time and it just stopped working?
There is an ongoing issue with the Windows version of 360 not opening for many users. Check this thread. Norton 360 will not open - Norton 360 for Windows - Norton Community
Your issue on the iPhone may be related to this thread. Keeps signing me out of Norton on my iphones - Norton 360 for iOS | Android - Norton Community