The black connector came off the power supply

Well, you have managed to dislocate the connector from the circuit board. The connector is fine, but:

A few possible things can happen.

1. the copper pads come off the PCB.
   1. you can fix this by locating where the copper traces go to, and solder in wires to get an alternative path. This is quite advanced.
2. the connector separated from the copper on the PCB
   1. You can solder the connector back on. Thsi is also quite advanced, the pad for the connector is likely underneath. Or:
   2. solder ribbon cable to the pads meant for the connector (I have seen manufacturer do this to cheap out)
3. The connector is a thru-hole component, and you managed to destroy it.
   1. This mostly follows possibility 2. Thru-hole pads are a lot more difficult to destroy, as it anchors into the board itself.
4. Nothing is permanently damaged, the plastic slip off of the contacts.
   1. This is the best case scenario. You can just carefully push the plastic back to its original place.