PIC16F627 has a PGM pin, and can work on LVP mode. Having the LVP mode set to off in your config fuses is not enough in many occasion, you also need to pull this pin to gnd with a resistor.

See the following link

http://www.microengineeringlabs.com/support/icsp.htm

And see what note 4 says...
4. Make sure the "low-voltage programming" pin is pulled to ground. Low-voltage programming is not used by melabs programmers and should always be disabled in the configuration settings. Even so, the low-voltage programming pin (labeled PGM or LVP) should be pulled to ground when programming. If it is left floating or in a high condition, it may interfere with the programming process. ...
Also make sure of your connection, As far as I remember, Pin 1 of PICKIT 2 is the pin with the white arrow on.