Hi and thanks for the help. What I ended up doing was advertising it on
our local version of eBay for a dollar and, when it didn't sell, I
reckoned that was a karmic sign, so I used a bit of reverse psychology
on it. On the basis that it had stopped working after power was removed
for three weeks, I disassembled and reassembled it so that it would
power up (as described in my original post) and then just left it
connected in a powered-up state overnight (displaying the "Sharp"
logo), before trying to operate it or press any buttons.

In the morning it was working perfectly, and still is a week later.
Strange.

If it fails again I will certainly try replacing the capacitor. In the
meantime, this baby's never going to have power disconnected again!

Thanks again to you both for your help.