First, remove C14 from the board until a suitable replacement can be found. It is not critical to the operation of the board. You just want to make sure that the cap doesn't swing around and short something else.
The replacement for C14 should be a 1uF MKP capacitor but any 1uF film cap rated for 50v and up will suffice. It's just for supply filtering so exact choice isn't too crucial.
Secondly, desolder the wires for the LED from the board. Again, the LED isn't crucial to board operation. Alternatively, look at the edge of the board right above the 'B22' marking. The LED is soldered there. Clean up the unconnected pad (with part of the broken wire in it) then strip a short length of wire from the LED wire that came loose and resolder to that pad.
The most important part is to make sure the ground wire is soldered back in place. There are 2 locations on the board for the ground wire. Soldering to the ground pad on either of these 2 locations will work but the wire is probably only long enough to reach the nearest one. From your pictures, it looks as if the ground wire is dislodged from the left channel board rather than the right channel board.
Last but not least, it seems that the supply wires are soldered from the bottom of the board. Verify that the wires are not dislodged or shorted.