The fact you pc runs for 10 minutes before it starts its reboot cycles, sounds like a overheating problem to me.
Does the pc do the same when your not connected to the Internet? If you simply switch it on and let it run, will it reboot again?
If not, then it could be a virus/trojan problem that activates itself once your connected. If it does the same, then I'll look into the hardware.
Check your CPU fan, chipset and video card for problems. I'll also suggest you download a copy of the hardware testing program available in our download section.... leave it running until it comes up with a problem.
Once you get your results, post them back here so we can check them.
Cheers,