Now that the old wobbly jack is out, pull the rest of the wires through the hole in the frame.

Then feed the wires of the new jack through that same hole.

On my replacement, there was a ferrite bead halfway along the wire, wrapped in shrinkable tube insulation, which together was too large to feed through the case. I had to carefully snip away the tube, feed through the wires, and slip on a fresh piece of 10mm shrink tube from the other side.

The new jack should go in easier than the old one came out. Make sure it is aligned the same as the old one with the wires going away from the screen, and snap it in.

Then put that metal cover back over it and place the short wire with the ring terminal on top of that, then re-install the screw through that connector and tighten it down.

Beware: On my replacement jack, the metal cover was so tight to the positive wire (nearest the top of the jack) that it shorted out after reassembly (the green light on the power brick cut out as soon as I plugged it in).

I used needle nose pliers to open out the right angle of the metal cover, away from the wire, and added a small piece of insulating tape under it to prevent shorting.