I had this problem 4 weeks ago.
To solve it you will need to run a number of different anti-virus program scans because you need to eliminate a backdoor "Internet Relay Chat" program that a rouge internet site has planted on the machine.
I'm suggesting here, but I bet the internet connection will freeze, sometimes after 20 seconds, sometimes after 5 minutes, sometimes after one hour? And sometimes the BSOD will appear just like you have outlined.
Mcfee will not see it and will report your PC as clean. Try 'Stinger' (its a Mcfee free download - about 2 meg). If it does not see it then try another free virus scan. Got to
www.majorgeeks.com and hunt through the many free virus checkers that are safe and tesgted by the site.
Then get protection suchas Zone Alarm, SpyBlaster or SpySweeper etc.............
Good Luck
Craggs