Definitely uninstall Norton. It is notorious for hogging resources and slowing systems down. What's more is it's really not that good at detecting viri. That should be first and foremost on your list.
Once it's uninstalled go here and d/l free Avira: http://www.free-av.com/ It's honestly one of, if not the best antivirus program available.
Next ensure you have nothing plugged into your USB ports while booting. Plug stuff in after you've booted that you'll need during your session.
Download and install Ccleaner found here: http://www.google.com/url?q=http://www.ccleaner.com/download&sa=X&oi=smap&resnum=1&ct=result&cd=1&usg=AFQjCNGSbcQ6KcnsjlF5Y2QL4CkB3Ya2oQ
Now analyze and run it.
Remove unnecessary items from the start menu. To do this type “msconfig” in the “run” box and hit enter. Choose selective startup and uncheck all of the programs that you do not need to load every time you start your computer. This will make the computer start more quickly and efficiently. DO NOT uncheck items that you do not recognize. This could cause you computer to run improperly.
Ensure you don't have resource hogging "trial-ware" or spyware on your pc (see step above.) Some examples are (but not limited to): Adobe speedloader, Yahoo messenger, various "smiley" type programs (that create smileys) etc. Take 10 minutes and research what types of programs you may have installed to ensure they are not bloatware and if you can live without them.
Finally and this should be the final step, defragment your hard drive (and continue to do so regularly!) Click Start, select All Programs, select Accessories, select System Tools, click Disk Defragmenter.
(or)
Open your Windows Explorer and view all drives. Right click on the drive you want to defragment and select Properties. In the Tools tab choose Disk Defragmenter.In the Disk Defragmenter tool box, you'll need to select the hard drives you want to defragment. In Windows XP you can Analyze the drive first. A user interface will show you the progress as you run Disk Defragmenter. In Windows Vista there is no graphical view of the progress as the application works.
If you have XP and it tells you your disks don't need to be defragged, do so anyway. I would advise you to get a program called O&O defrag, but it does cost money. It's head and shoulders better than the default windows defragmenters, but alas it does cost money to purchase. Any The Disk Defragmenter tool can take anywhere from minutes to hours to run, depending on the size of your hard drive and also how fragmented the drive is, so be prepared for the time involved here. I personally defrag my hard drives over night, while I'm sleeping.
All of these steps above will take some time to complete so be prepared to spend some time on it, but chances are your pc didn't become slow over night. I personally think you'll see a huge difference once you uninstall Norton. By the time you are finished with the above list however, you'll be amazed at the difference in boot times and the overall performance of your machine.