iFixit troubleshooting guide gave me the confidence that the power supply was most probably the problem, Seemed a shame to let a perfectly-good computer die.
The old power supply removal instructions could have been more detailed. (see below)
A few scary noises when trying to put in new supply.
Now works perfectly.
Should have suggested that the long hold-down screws be loosened and then pulled completely out with needle-nose pliers before moving the old power supply.
Need clearer instructions for dealing with light sensor cable.