Problem with Random Reboots

Get your hands on another anti-virus, along with an anti-spyware (or 2, I personally run Ad-Aware Pro, and Spybot Search & Destroy, first one's paid but there's a free version, spybot's free), take your PC off the network, and scan like crazy. No anti-virus or anti-spyware is 100% effective, and on rare occasions can become corrupted themselves so that they appear to work properly but actually let nasty things run rampant. Your best bet would be finding one you can load from a CD made on another (clean) PC to eliminate the possibility of corruption, but I'm not totally sure where you'd find one of them (in fact if anyone knows, feel free to reply with info!)

Also, get memtest to make sure your RAM's still working and hasn't developed a fault due to old age. I'm guessing that's your problem if your total physical is 512 KB... sure you don't mean MB? 512KB would be a lot for windows 3.1's era, but now it's what you make fun of at parties with 2GB RAM sticks. Wait, I'm the only one that does that?

Just another though - download CPU-Z and tell us what the CPU's actual name is... x86 Family 15 Model 3 Stepping 3 Genuine Intel doesn't mean much to most people on here. I'm thinking it's a ~3 GHz Pentium 4 though, but that's just a guess  

Give us the rest of your system specs, and be specific, motherboard, PSU, hard drives, graphics, etc. etc. etc.

start in safe mode, with anti virus and spywae already down loaded but not installed - install and run

runs msconfig and turn off the stuff in start up accept what is ms or anti v or anti s - should be 6 things or so

hide ms in services in msconfig turn off all but anti v and anti s

too many start up programs suck up the memory

add more memmory
add more voltage to memory - it needs it as it ages

replace it or run memchek

If you are not 100% confident to go trouble shooting you could always try the fresh install of Windows..... chuck in some extra ram and you will be up and running as good as the day ou bought your pc.

Norton used to be notorious for causing system instability on lower spec pc's - loved to use as much system resources as you would like to chuck at it.

360 is much better - so dont think thats your problem. Open task manager (CTL + ALT + DEL) - check the performance tab to see if your CPU is runnning maxed out at 100% if it is then chances are it could be spyware / virus. While you have the task manger open check how much physical ram is free / and how much virtual memory you are using.

If you are lucky it could be just a RAM upgrade...

just a quick thought..... have you checked inside your case - in particular the HSF on top of your CPU ? dust is a sure fire way to cause heat / shut down problems.