Without schematics, can anyone suggest how I might go about determining a
suitable replacement LED from an electrical perspective?
Or, if you can find even one working LED on the original panel, remove it and
connected it (correct way round) with a 330 Ohm or 470 Ohm (or so) resistor
in series to an adjustable bench supply. Turn up the supply until the LED is
glowing at what you consider to be normal brightness (this will be 5-10V I would
guess). Now measure the voltage across the LED itself and the current through
it (or deduce the latter from the voltage across the series resistor and the known
value of that resistor). Try to find an LED that matches those values for forward
voltage and operating current.
Or as I said, just stick in standard red LEDs. I've replaced LEDs many times without
thinking what I am fitting.
-tony