My advent T9207 keeps restarting at random times when connected to the Internet.?

Make sure the machine is well ventilated, you could be suffering from too much heat. Try running it with the side off to see if this helps. If not and if it is only whilst surfing the net, try using a different browser like firefox etc, if this fixes it, it will more than likely be an IE (or add in) problem. You can then uninstall Internet Explorer and re-install.