@hannesw sure! I didn't dwell on it much in the video, but the symptoms were:
1. Device doesn't switch on when cold
2. Device switches on when circuit is warmed
3. Device works normally once switched on (even when cold)
That points to a fault with the "starter" capacitor on the switch mode power supply. These are usually a small-ish electrolytic (~10-47uF) with a high-ish voltage rating (~20-50V). They're energised continuously by the supply voltage, so are prone to failing early - especially in the UK where our supply voltage is often >240V.
So it was a case of finding that particular cap. I was lucky to find a report of another Linn with the exact same fault (although the capacitor was elsewhere on that particular power supply). After that, I just had to find the suitably-valued electrolytic nearest the switch mode chip...