Once you're satisfied your keyboard is now fully working, turn it off, re-install the thin metal plate and use superglue to replace the welds and hold it down. Apply firm pressure while the glue cures so there are no gaps.

This will take a while, but it's worth doing properly because those welds were important! They stopped the entire keyboard from popping out when you press on a key. The superglue will suffice and with the added benefit of being easily removed if you need to re-enter the keyboard.

If the adhesive on the back of the plate is still in fairly good condition, you should be able to stick the white plastic cover back on. If not, use a little glue.

You can now re-install the grey plastic cover and every single key on the keyboard. To do this, apply pressure between two fingers to clip the keys back on, one on the underside. This will stop the glue from breaking.

That's it! Test it again to make sure it works. If it does you're clear to start using it again. Just be mindful that the structure has been compromised. Smashing your fists on the keys at any time will undo your work gluing it back together.