I finally managed to borrow a PSP charger, and the same thing's happening - plug it in, the red light comes on, and then goes off after a few minutes.
So now I'm wondering - is the battery not charging at all? Or is the battery fully charged, and the screen is actually faulty? (There's 80Mb free, so I don't think that could be an issue; and I don't have any SD card in).
Is there any way to check the battery via software? Neither the Sony software or Calibre seems to give you any information about the reader itself.
I'm just trying to figure it out if I have to send it away for repair, or not - I'm going on an overseas trip in 3 weeks, and it'll take 6 weeks to repair
Edit: thinking about it, it can't be the screen. Because then when I switch it on, the screen might be blank but the little light would be on. At the moment, that's off. So it must be battery related, somehow.