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I think that, if this is the case and you retrieve the socket you should be able to glue it back on and add a dab of solder at the 5 points to reconnect the connections.
It looks to me like only the 3 closely spaces pads in a line would need to be soldered if you've glued the connector down; the other 2 look to be just for physically fixing the connector.
Nick.Earthloop-
Yep, could be. A photo of the unstuck socket may shed some light on it. The danger with the soldering is that you don't melt the existing solder and loosen what ever is connected on the other side of the board. I tried to solder something similar before in a hurry and let's just say it didn't work.....this may be a more foolproof option: http://www.maplin.co.uk/p/circuitworks-conductive-pen-standard-tip-n73aa
Matt101
Comparing your photo with the ones in this link, it appears that you may have ripped off the battery socket from the garmin when you removed the old battery plug? On the top right corner of the circuit board in your photo there should be a plastic socket for you to plug the battery into. Instead there's just 5 spots of solder........: https://forums.garmin.com/showthread.php?33752-Edge-800-Replacing-Battery-Pics-and-some-info-not-complete-yet/page2
If you have the old battery see if the socket is still attached. From memory, the angle you pull the battery plug away from the garmin is key. In one direction it comes away easy, in others it won't and you may well pull off the socket with the plug.
I think that, if this is the case and you retrieve the socket you should be able to glue it back on and add a dab of solder at the 5 points to reconnect the connections.
Let me know what you find......