normalizing STFT output and calculating energy of signal
The STFT yields complex values. Energy conservation (up to a scaling factor) should apply to the square of its magnitude, also called spectrogram. Depending on 


the initial normalization of the FFT, 
the window shape,
the lag (do you compute the FFT every $h$ sample, $h$ is called the hop, sometimes), 


the scaling factor will differ, but will be the same for all signals.  


$2$/window length is specific to a choice of the three parameters above. A scaling factor will only result in a $\log$-magnitude shift, which does not really matter for display or relative energy.
If you can compute the energy normalization based on the three parameters above, good. If not, take a randomly-picked signal (non zero), compute the ratio between the energy of the signal and that of the spectrogram, and you have your factor. Beware of the border effect, better take a centered signal with enough zeros (above the window support) on the right and the left.