The startup process you described sounds like what happens when the computer shuts down improperly. Were your options something like: start Windows normally, start in safe-mode, start in safe-mode with networking, etc.? Are you shutting down the computer properly before you start it up and get this? How many times did it happen at your house? Every time? How many times is that? How many times did it start normally at your friend's house?
It's not your monitor. And I don't think it has anything to do with the Internet connection, but I really don't know if it's possible that any of the pre-installed junk could have registry or BIOS entries that are making it try to establish communication with the outside world during the boot procedure.