Norton is a resource hog and I would bet the large amount of cpu cycles at start up is Norton.
How must memory do you had installed on your system?
In any case do a control alt delete and bring up the task manager and then go to process tab and check for what processes is using the most resources.
Go to the control panel and then the admin tools and event viewer system and look for events mark as errors in the log. With special attention to any errors in connection to the virtual memory/pagefile.
Report back pleases.
As far as a virus and malware is concern I would go to the following link and following directions created a cd boot disk of microsoft system sweeper and boot the computer with it and run a complete system scan if there is a virus or malware including root kits is will deal with it.