I broke the SATA connector on one of my Seagate 320 Gig drives. The plastic part was still in the SATA cable. I hot glued the cable onto the drive. As long as the drive or cable is not moved it works fine.
If the pins are good and you have the plastic piece in the cable they should make contact. You can get the data off the drive. IF you have to you can cut one end of a SATA cable and as long as you solder the correct wire to the correct pin you can do that if you have to.
Pins 1, 4 and 7 are grounds, Most of the time they are just bare wires in the cable. Pins 2,3 (TRANSMIT) and 5,6 (RECEIVE) are the data wires, Just make sure you do not cross the wires. The data cables have plastic over them and they are inside shields. I have cut and soldered the wires to a SATA drive to recover the data for a friend before.
The pin outs are available on the net and with a multi meter you can ensure you have the correct wires, I put electrical tape between each pin as I soldered them so no contact occurred between the wires. It takes a fine solder gun and very little solder and a steady hand.