Can you make the microphone work by putting a bit of pressure on the cable connector with the cable inserted? If so, you may be able to hold the cable in, in the correct position, with a few 'dobs' of neutral cure silicon sealant between the connector, cable and mainboard. You don't have to smother it, just enough for it to maintain connection and to stop it from moving. Make sure it works after applying the sealant, allowing a bit of time to set first. If it works allow as much time as you can, for the silicon to 'cure' (set or harden), overnight should be sufficient. Do not use 'superglue! If it doesn't hold the cable in position properly, you are stuck, literally. Also it may react with the 'plastics'. With neutral cure silicon sealant you have a bit of time to get things right and it is relatively easy to remove.
Hopefully this is of some help.