Of all the possible things that could have fouled up my attempt to repair my laptop, I didn't foresee this one.
Thanks so some rather robust German over-engineering, it seems like they used case screws made out of titanium and got them tightened by The Hulk, because they ruined my mini-screwdriver (literally sheared off the edges of the turning planes) by the time I attempted to remove the third screw. Out of nearly THIRTY. At that rate I'd be spending a fortune on new screwdrivers simply to open the little bastard up.
So I didn't even manage to take the case off, let alone have a go at repairing the power socket with the soldering iron I was so looking forward to using. Sigh. I guess I'll just have to find a decent independent PC shop that repairs laptops.