I think that if you erase the old python.dll file from system32 and syswow64 folders, (keep a copy of these files to revert the proces just in case) and then install again python from the installation dvd, this could fix your problem.
I took the python.dll file from the other computer were Argis+python were working fine, but if you don't have another computer with arcgis running, try to do what I say in the text above.
References:
-NOT WORKING python.dll ----->creation date 11/april/2012------->size 2918KB------> REMOVED
-WELL WORKING python.dll----->creation date 10/april/2012------->size 2250KB ----->PASTED TO SYSTEM32 FOLDER
add these strings
PYTHONHOME=C:\Python\ or C:\Python25\
PYTHONPATH=C:\Python\Lib;C:\Python\DLLs;C:\Python\Lib\lib-tk;C:\Python\Lib\site-packages
at your system environment path and python should work fine
Check your correct python folder the modify these paths above.
PYTHONHOME=C:\Python\ or C:\Python25\
If setting a PYTHONHOME environment variable, it will need to match the actual installed instance of Python you are attempting to use. For most, with Python as installed with ArcGIS 10.2 or 10.3 that would be C:\Python27\ArcGIS10.x (the x version installed). ArcGIS 9.3 used Python25, ArcGIS 10.0 and 10.1 used Python26.
PYTHONPATH=C:\Python\Lib;C:\Python\DLLs;C:\Python\Lib\lib-tk;C:\Python\Lib\site-packages
With a PYTHONHOME set, the PYTHONPATH environment variable could also be %PYTHONHOME%\Lib;%PYTHONHOME%DLLs;%PYTHONHOME%\Lib\lib-tk;%PYTHONHOME%\Lib\site-packages. That allows changing from one Python install to another--trivial--just change the PYTHONHOME.
Windows is a strange beast in that the Python installation will place pythonxx.dll into the C:\Windows\System32 on a 32-bit OS--but on a 64-bit OS the 32-bit library goes into the C:\Windows\SysWOW64 folder, not the System32.
And if you elect to install the Esri 64-bit background geoprocessing extension--an additional 64-bit Python is installed, then a 64-bit python27.dll will be installed to System32. The two DLLs have different date/time stamps and sizes, don't mix them.