Can't connect to app store after installing VPN software
Interesting.  If you are on Lion, which you seem to be from the screenshots, then you can first try:

man 8 softwareupdate

softwareupdate -l 


Would ordinarily list your available updates.  But wait!  Open another tab and in this one you are going  to use the handy nettop(1) command  

Just type "nettop" and see what it says.  Do not quit, use down arrow to see the bottom, use left arrow to summarize.  Do not quit.

Now run

softwareupdate -l and see if anything proper happens _on the nettop tab_. ( Paste it here I guess ) 


The first thing we can try with lion until the next os:

man sysdiagnose  # handy as a gun in a knifefight


There will be no secrets, I believe.  

Trivia:

man 8 tmdiagnose
man 8 mddiagnose # spotlight 


This is a painfully obvious thing to ask but,

did you try looking at the Console.app?  Or typing 

syslog


to see what osX thinks the problem is ?

syslog -F raw -w 20.


will make it act like tail -f

Finally, you can reach for the rum, the chalk, and the chicken and use, if you are using wi-fi that is:

airportd   #there is no man page for this

airportd prefs  # see what is set

airportd readNVRAM # see what your fallback network is set to.


Have you tried rebooting and holding down cmd-R, to get to the recovery partition?  The main drive is not mounted,  it's very cool, assuming you did not have a custom partioning scheme...