How odd, the shutdown problem which you were describing at the beginning of your post sounds a lot like the infamous blaster worm which infected a lot of computers in the summer of 2003 I believe.
I wouldn't be too concerned about letting the systemreg16 file access the internet, I run zonealarm and get that every now and then, and I haven't had any problems with allowing it to access the internet.
I skimmed through your log and all appears fine.