You should not restore it if it is confirmed malware. It is in quarantine now which means it cannot do anything anymore. Just run a full system scan (make sure that Norton is configured to scan all files) to see if Norton will find anything else or any related malware to what it has quarantined.
If you want to doube-check that there's no more infection, run an online scan using online scanner.
Also, when the system is confirmed clean, you should re-enable System Restore.
I have a backdoor.irc.bot in quarantine under Norton 360. With this bot in quarantine am I safe for online activities like banking and email?
I've done virus definition updates and tried to do the scan in safe mode but the Norton 360 does not allow safe mode operations. I got on another thread with Windows Vista asking how to remove it but it is unclear what files I'm allowed to delete. This backdoor bot has attached itself to 6 processes, 2 files, 68 registry files, 138 host file entries and 1 browser cache. The instructions I got told me to go to the system restore and shut it off. I did, then do a scan; well now I can't find the bot because it's in quarantine. Am I supposed to restore all the files it's originally attached to so that I can try to kill it with another av or malware software?