System locks up when on-line

Hello all,

 

Recently, I ran into a problem with a PC at home.  Whenever this computer is on-line, the computer will lock up at random after some time.  I've formatted the hard disk and reinstalled the OS, but the problem came back eventually.  A test was done by disconnecting the computer from the internet and it ran all day without locking up.  However, as soon as the internet connection is restored, the system will eventually crash. 

 

Now recall this PC was formatted and I performed a clean install.  I believe something out there is locking on to this PC and causing the system crash when connected to the internet.  Unfortunately, Norton did blocked some random attacks as it display message attacks blocked.  However, this one core problem is somehow getting pass Norton. 

 

Finally, I have not spend much time reading on this forum, so I'm not sure if anyone else had this problem.  I would like some recommendations on what I can do to restore the PC to be able to work while on-line.  Number of tests were done, and at this point, I'm sure it's an issue with out side attacks that is crashing my PC whenever it is on-line.  Thanks.