Just a little update: I finally got a chance to buy a replacement capacitor, and it's working again! (so far...) I replaced the bad cap rated at 10v and 680uF with a 10v 1000uF cap (the closest that the shop had).
Yeah, the design of the US version looks like it makes the procedure much more straightforward. I have the UK version with 2 SCART sockets.
Your tip about the VHS door was a huge help, thanks. I would never have noticed that until I had reassembled the unit and noticed my mistake!
The only difficulty I had was that I also cleaned the spindle in the DVD drive, and I replaced the lid incorrectly, blocking the mechanism that allows the tray to come out. The only way I could rectify this was to power on the unit without the lid, open the tray, shut off the unit (and disconnect power), and then replace the lid.
Thanks again VoxHumana, it was actually thanks to some of your old posts (as DigaDo) that I got the idea of trying to replace bad capacitors instead of just throwing out the unit! It's really cool that you're so generous with your time and knowledge helping people keep their older machines running.