First thing to ask is are the definitions up to date for your Spyware and virus scanners ?
The reason I ask is that there are a few virii that use your Internet connection to bombard other sites to try and overload the server. The side effect if that your Internet activity suffers big time and becomes almost unusable.
My old 1GHz Athlon that runs 24/7 collecting Emails slows down after a few days but still remains usable but you do get a few seconds delay after clicking a link before anything happens. If this case I think there is a memory leak and as the swap file is a fix size I think resources get low. But the machine is scanned everyday for Spyware ,adware ,and Virii .Plus the programs are set to look and auto update daily.
If you haven't got a Virus scanner (that includes Norton ) ,the goto
http://free.grisoft.com and download the free AVG version 7. If your connection is being used for other things it might take a while but it'll be worth it.
As you can see I don't like Norton Anti-virus for the main reason that that is what is installed on a lot of PCs I see. And it either never gets used or is well out of date. It comes with some new PCs and people don't check that it's actually doing stuff. Plus the security suite needs a subscription which when it expires stops protecting you !