Motherboard Issue. Fixable but I need advice

Power Connector on motherboard came off while removing ribbon. The plastic piece stayed on the ribbon while I was trying to remove the ribbon. I even used the proper removal tool.

HERE'S THE LINK FOR PICTURE

iPhone 4S Teardown

It is step twelve, the black housing all the way to the left and has 4 pins in it.

Should I get soldering glue in a syringe and put it back together? What type of solder? I know I'm not out of luck, but seeking the best way to repair. I have zero experience with circuit soldering.

NOTE: If I push down hard enough (to allow contact), I'm able to get juice and power on the phone.