The Python packages shipped with QGIS live in \path\to\QGIS\apps\Python27\Lib. So you need to add that to PYTHONPATH, rather than ...\qgis\bin.
It is best to do this on script-basis, rather than system-wide, like so:
import sys
sys.path.append("C:\Program Files\QGIS Pisa\apps\Python27\Lib")
import qgis.core
But be aware that the QGIS Python packages were likely built for a different version of Python. So things might not work smoothly.
Note: QGIS Python plugins are installed here: ~\.qgis2\python\plugins, so you might need to sys.path.append that too.