Amaury, when I tried to run IDLE from the command line as you suggested
I got:

C:\>C:\python26\Lib\idlelib\idle.py
IDLE Subprocess: socket error: An attempt was made to access a socket in
a way forbidden by its access permissions, retrying....
IDLE Subprocess: socket error: An attempt was made to access a socket in
a way forbidden by its access permissions, retrying....
IDLE Subprocess: socket error: An attempt was made to access a socket in
a way forbidden by its access permissions, retrying....
IDLE Subprocess: Connection to IDLE GUI failed, exiting.

...followed by 2 error windows:

Socket Error:An attempt was made to access a socket in a way forbidden
by its access permissions

and...

IDLE's subprocess didn't make connection. Either IDLE can't start a
subprocess or personal firewall software is blocking the connection

...BUT when I try to run IDLE from the "all programs" menu it runs just
fine - which it did NOT when I created today's bug report.

To try to reproduce the original behavior, I first put back the unfixed
version of run.py and IDLE STILL RAN FINE from the program menu 

I was VERY confused at this point and I completely uninstalled Python2.6
and reinstalled it from the same .msi installer I used before.

After I reinstalled 2.6, IDLE again ran fine from the programs menu
WITHOUT making the fix in run.py but NOT from the command line -
producing the same error messages as at the top of this entry.

Right now I am so confused I don't know what to do. I cannot reproduce 
the original problem I reported in this bug report and IDLE runs fine
from the menu but not from the command line.

It know that IDLE would not run from the programs menu until I changed
run.py but once I did that, removing the fix seems to make no
difference. (I've been careful to remove the run.pyc file each time.) I
believe that the behavior I saw today with 2.6 was the same as I saw on
Sept 22 with 3.0 when I submitted #3943 - and with the same confusing
property where the fix is needed to make IDLE run but removing it makes
no difference.

I hope this makes sense to you. It doesn't to me.

...Bob