The wonderful ozisim saw me whinging woefully on LJ about this and said: what you need is SUGRU! And not only did she suggest this, she posted me some, which was a true Act of Kindness.
It comes in a little silver packet, and feels a bit like plastacine. But unlike plastacine, it sticks to things quite enthusiastically, and it hardens when left at room temperature to a tough, rubbery substance like those silicone baking tools. And it is *exactly* the stuff you need if some poorly-made component needs to be stuck back together in a way that will hold it together longer term. My laptop has not lost power once since I Sugru'd the power supply back together.
I thought about photographing the repair, but that would be pretty dull. However, I did have some sugru left after repairing the socket, so I thought I would try repairing the bit on the outside of the case where there used to be a bunch of plastic bars over the air intake, but most of the plastic bars have snapped off. I thought if I tried to make plastic bars of sugru, they would inevitably look a bit saggy, so I decided to roll with the sagging, and instead make a sort of Cthuloid grille thing. I did not, honestly, expect this to stay in place. I thought it would probably fall off overnight. But it's still there a week later, and it seems to be amazingly robust! I wish I'd put a bit more effort into making it now.
In short : Sugru is Amazing. And anyone who tells you that whining about your minor technology woes on a blog is a waste of time, is WRONG. :-D