If the CMOS battery (the one on the motherboard that regulates among other things the time and date of your system when turned off, and remembers the system configuration as well) were on the way out it wouldn't speed up. The PC would give you a warning when you boot up that the BIOS settings were out (or words to that effect) and then you would constantly have to reset the time and date when you get to Windows as this would revert to something like 01 01 99 0000hrs
you've confirmed this
I have been into the set up screens and tried the clock in CMOS. That is running at normal time and normal speed.
..so it's definately not hardware related. That leaves software. If Norton is no longer working then it is probably virus or spyware related. PC World are a joke, they're answer to everything is reinstall and the 45minutes on the phone probably cost you a fortune. A reinstall will certainly do the trick but...
but that leaves you with a machine back to factory condition and you will have to setup all your applications and software again, including the internet.
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If it is virus related;
download combo fix and save the file to your desktop > <a class="postlink" href="http://download.bleepingcomputer.com/sUBs/ComboFix.exe" onclick="window.open(this.href);return false;">http://download.bleepingcomputer.com/sUBs/ComboFix.exe</a>
Download Spybot search and destroy > <a class="postlink" href="http://www.safer-networking.org/en/mirrors/index.html" onclick="window.open(this.href);return false;">http://www.safer-networking.org/en/mirrors/index.html</a>
Restart the computer in safe mode > press F8 when booting, choose Safe Mode with Networking
Then run combo fix (just follow the prompts, accept the agreement but you don't need to look for updates or install the Windows Recovery Console). Takes around 10 minutes to run and produce a log.
After that run spybot . Allow spybot to fix whatever it finds if anything.
Once those are done reboot, if the pc starts to play nicely again download AVG Free Edition > <a class="postlink" href="http://www.free.grisoft.com" onclick="window.open(this.href);return false;">http://www.free.grisoft.com</a>
Then run AVG (full scan). Once AVG has done it's thing, uninstall it as you shouldn't have 2 AV programs at the same time due to conflicts, compatibility and system performance.
Last thing > download HiJack This > <a class="postlink" href="http://download.cnet.com/Trend-Micro-HijackThis/3000-8022_4-10227353.html" onclick="window.open(this.href);return false;">http://download.cnet.com/Trend-Micro-Hi ... 27353.html</a>
run the program, copy and past the results into notepad and past them here. I'll look at the log. Last things then are emptying temp files and folders, and purging the restore cache. I'll go over that after the machine is working okay again.