Welcome,
Before trying to install 360 on your laptop please run
The Norton Removal Tool to clean out the expired NIS software. After rebooting you can then do the 360 install.
If you don't need a proxy [you didn't set one up or your network administrator doesn't require one] eliminate the settings.
If you think that you may be infected now you can run a scan with
http://www.eset.com/us/online-scanner/
then do your 360 install
After activating 360 be sure to run live update to bring it up to the minute
is the link for an almost current copy that you can download and activate with your key
Keep us posted