Check your memory is OK
Just a thought - if you upgraded your memory, remove the upgraded modules or try it with the old unit/s and see if you still have the problem. Incompatible memory modules often bring about the same system slow-down. But first check the SYSTEM box on SETTINGS and make sure that the total Memory Capacity shown under the Windows System info agrees with what you have installed (quick common-sense check that it is working and up to speed).
If it is a Norton problem - some computer makes and mixes of software just don't like Norton. McAfee is a good alternative [and you can put as many copies on as many computers as you like if you have an account with them].
Also check for spyware - as nasties of this nature drag your computer to snail-pace. If you go onto mcafee.com and search 'stinger' it will give you a weblink for a downloadable stand-alone nasty-hunter (Stinger AV) that will quickly and painlessly scan your computer for nasties.
If you still have problems, your Operating System (XP?) might have been corrupted by a virus/trojan and require reloading. Hope not!
Remember that some viruses which can also cause such performance problems often hide behind the SYSTEM RESTORE firewall, so unless you turn off your system restore (MENU/SETTINGS/CONTROL PANEL/SYSTEM/SYSTEM RESTORE) every now and then, scan the whole C drive [and afterwards reselect System restore again (through Help & Support Menu)] you will never get to the little bugger as it will constantly re-infect on booting up!
Good luck!