Start by cleaning out your computer - literally -> Open it up and remove any/all dust. You will probably want to do this outside or in the garage.
Dust is a major cause of overheating and may well be the cause of many of your problems.
Next, make certain that all the fans in the system work properly. If any aren't working, you need to replace them.
I tend to think that if you had a virus Norton would have found it, however, it never hurts to try something else. Here is my guide to virus removal:
Top 3 free AV products
Avast
Avira
AVG
Best Paid:
My recent survey of several independent testing labs shows Kaspersky and BitDefender as the top 2 paid AV products.
How to remove a virus -
I) The best solution is to back up your data and perform a factory restore. Install a reputable AV program after the restore and download the latest updates before restoring your data.
II) That not being practical for many, try either of the next two methods:
(Please note that it is important to use one of these two methods as you need to boot and scan knowing that no viruses are already in memory. If you try and install an AV product on a machine already infected then there is a decent chance that the virus will be able to hide/relocate from the scanner.)
A)
1) On a clean computer, download 1 or more free bootable AV products. Five I know of are Avira, AVG, Avast, Kaspersky, and G Data.
(There is a handy product called sardu (www.sarducd.it) which will create a flash drive/Cd capable of having multiple AV products built into it. It isn't perfect yet, but it does do the job pretty well. I keep a copy on a flash drive for whenever I go to someone's house to help with computer problems and I have a number of other diagnostic tools included as well.)
2) Create the bootable media and include the latest virus definitions
3) Boot the infected/suspect computer by using the bootable media and run a full/complete/deep scan of the computer using preferably at least two different ones. No AV product gets them all, but 2 different products should find and remove just about anything.
B) second alternative method:
1) remove the hard drive from the infected computer
2) slave the drive to a clean computer which already has at least one AV product already installed with the most current definitions. You can do this by installing it into the case (for a desktop) or by putting the drive in an external drive case which you can get for the low teens $. These can be USB (get at least USB 2.0) or eSata - if the 2nd computer has an eSata connection.
3) From the clean machine, run a full/complete scan of the slaved hdd. The computer should already be booted when you connect the external drive, with the AV product already in residential memory (it will have an icon down next to the clock). Then open the AV and run it on the drive. In an ideal world, you should really use two different AV products.
III) If you are unable to do the above, then download and install an AV product and then run it at its deepest level scan. This is not the ideal method as many viruses can hide from AV products if they are already in memory and running before the AV sofware is executed. There are numerous free ones. I strongly recommend two different AV products and one Adware/Spyware product. For free AV, I would typically recommend Avira, AVG, or Avast as the installed resident (always running) AV solution and Malwarebytes as a secondary, on demand AV product which I run on a weekly basis. For Spyware and Adware, the two top performers there are AdAware and Spybot Search and Destroy (adaware is a product of lavasoft and safer-networking.org produces Spybot Search and Destroy) Both offer a free and paid version. The free version is good, the paid version offers more bells and whistles, just like with the AV products.
Once the virus(es) is/are removed, change any and all passwords having to do with anything important like e-mail, financial-banking logins, etc. as those have probably been captured and sent to the author of the virus.