Problem with NFC on Arduino MEGA
It is likely that placing the GSM shield between the Arduino Mega and the NFC shield is interfering with the GSM antenna.  Antennas react in strange and usually less useful ways when large conductors are placed nearby.

You could try reversing the order of attaching the shields, or you could try spacing the shields further apart using "stackable Arduino headers" (you can do a web search for suppliers).  If there is an option for an external antenna, that would be even better.

If you get GSM working, you might still have some trouble with the NFC shield, as it's possible that the GSM transmitter being so close could interfere with the NFD's circuitry - not because they use the same frequences, but just because any conductor so close might pick up electrical noise, and there will be various sensitive circuitry in the NFC electronics.