I have had a problem simalar to this were the result was a VIRUS, now when the computer tries to access the internet while no adapter is plugged in then nothing happens as your computer hasnt actually accessed the internet at this stage but when connected it does and this virus was programmed to terminate your computers session nasty **** thing.
Long story short i would try to run some advance anti virus programs. Could also try this online scanner
http://housecall65.trendmicro.com/
The other thing that has happened to me in the past is that the version of internet explorer would **** its self only when connecting to the internet. Try using an older version.
And last but not least Press and hold the windows key, followed by the Pause/Break key, this will open System Properties. Click Advance then click the settings button under Start Up and recovery then untick Automatically Restart button under system Failure.
What this will do is determine if it is blue screening, if it is you will see the code take picture or write it and send back to us.
Josh