Even a highly fragmented hard disk wont cause CPU usage to spike at random times, it will just make it take longer for the computer to open programs and files.
Also, AVG will do an okay job, but it can't detect everything -- especially rootkits (malware that hides itself by replacing or otherwise messing with system files) and some other types of malware. Your ideal computer will have ONE antivirus program, and one or more antimalware programs.
Anyways, can you find any common ties between the problems?
It could have something to do, for example with Flash (ie: if it freezes up a lot when pages utilizing flash applets are in use). Or perhaps FF/IE are using the same addon and the addon is causing a problem.
Could also be a driver issue, like if flash applets are utilizing video acceleration and the driver is flawed, or the ethernet or wireless driver hiccups when trying to establish a connection to a website.
Usually there is a cause of some kind, and this cause is from a recent change or activity to the system (like a recent windows update). It helps to be as specific as possible when reporting a problem. This includes going into the system/application logs (in XP you could view them by going to the control panel -> administrative tools -> event viewer) and posting any 'error' and 'warning' entries that it reports.
My point is, its important to trace any changes that happened to the computer at the same time the problem started occuring, and be detailed when explaining the problem -- the vaguer you are the harder it is for someone to help you.