After leaving this for 12 months, I started on it again.
So some progress for the benefit of anyone with similar problems. After repairing my power supply, the TV just restarts every 15 seconds as described in the earlier posts.
Go into the service menu, and disable the D-Watchdog. Voila! The TV doesn't restart.
But this leads to revealing the REAL problem - the digital tuner side of things is knackered. The TV will only scan and find analog channels, and when it tries the digital ones, I get screens of pink flashing 1/2 screen blocks with random digital noise.
Next stop - checking out the digital tuner side of things. On the LA40N81BD, there are 2 watchdogs....D-Watchdog and just Watchdog. I can have the Watchdog on, but the D-Watchdog off to stop restarts....so I assume D-Watchdog means digital watchdog. All HDMI ports work fine, just the digital tuner is kaput.