Re:
Okay, here is the lowdown - you cannot get the key until you have defeated Dakim on Mt. Battle AND you have given Sherles your P*DA number. Once you have defeated Dakim (and make sure to grab plenty of Ultra Balls and Revives from the Outskirt Station because you will need them and to save before your battle with Dakim) you should head on over to the mystery lab. Not very important now, but walk up to the gate and walk back and Sherles will e-mail you saying that they caught 2 Cipher peons. Go to the jail (make sure you have the jail key) and open up the cell with the two girls in it. There will be a girl lying on the bed go up to her head and talk to her. She is holding the key. The other one will just blame you so talking to her serves no purpose.
Team Rocket Lab
Chief Kyle