Lately I've struggled with my computer randomly slowing down at moments. When I check the processes of my computer I find that IE makes sudden large jumps in processing power that it consumes. I don't know why. Norman doesn't notice anything odd, well, that it can do something with. It finds two objects that it can't do anything with. I can't change anti-virus program as that'll void my warranty.

So... despite the lack of information and obvious solutions, does anyone have any ideas on what I can try to either speed up the computer or preferably eliminate what is slowing it down?

There's your problem right there. Solutions:

Firefox
Opera
Chrome
Seamonkey

Almost any other browser will do.

Firefox has some big memory leak issues if you don't close it down regularly.

I used firefox from when it started (until I recently made the switch to Chrome), and I never had a problem with memory leaks, even on my crappy old computer.

Problem identified.

Stop using IE. Its not faster, no matter what the drugs might be leading you to believe.

My Firefox tends to live about a month at a time without any noticeable issues.

And then I have to reboot for patches.

1. It's Norton, not Norman.
2. Changing AV programs voids your warranty? That's a new one!
3. Firefox is far more stable, secure, and more easily extended than IE. Only complaint I have about it is that it takes five times longer to load, but then I just don't close it unless I have to reboot.

Ha! That's what I thought yesterday when someone complained about Norman virus scanner or whatever...apparently it's a real programme.

I think Firefox' memory leaks are fixed already, but it used to have them for a long time.
Anyway...
Install and run Spybot, apply immunization, scan your pc for malware.