You did not state what OS you have Other than some MS bull****.. download an application called zonealarm not only is it the best firewall for the $$ it lets you block programs from getting access to the network (dial-up or via network - DLS - ISDN cable modem ex..) there is a free demo and it cost 35 a year to buy. To be honest this is almost the only software I own :p . "Black Ice" defender is good also but "Zone Alarm" ships with "PC cillin(sp)" and a couple other good privacy applications. FYI: IE stores your network browser history in more than one location thats very hard to delete.
AS far as killing that process that is running away check out the services control panel and see if there is any thing odd there.. and then just stop it. You should not be able to do much harm there, rebooting the computer will re-enable the services. I would guess that you may have an application (shareware - freeware) that wants to call home, or other such BS.
Good luch
