Thank you. Great idea, I will try to write something up.
Would this be a sensible approach? I crack the scope open, power it up, put a signal on ch 4 (the blown one) and e.g. ch 2, then follow the signal on both channels with my spare scope, and when ch 4 does not match ch 2 I would have found the first defect component?
Essentially yes, until you get to the differential pairs where they won't be ground referenced so some thought and care need be used for where to place the probe reference lead and how to do this. You may need to use a differential probe if you have one.
Hopefully you will find the issue before then and just connect the probe reference to one of the BNC shells.
The probe compensation square wave output should be fine to use for the test signal.
But before we get ahead of ourselves. the scope must come apart and yet parts need still be connected on the bench so it can be powered ON and be safe to work on. For extended ON time you need to provide cooling for some of the parts so you will need a bench fan.
Depending how it all lays out on the bench and if you can see the display you might need a mirror too.
There's every likelihood you can use one of the channels of the SDS2kX to trace the signal if you can see the display. A short custom link between the probe compensation output to the ch4 input could be handy to reduce the clutter on your bench.
And pictures, everyone loves pictures !
Take an analytical approach and work out where you need to probe, make drawings, study datasheets and mark test points with a fine Sharpie.
Where you in 50 Ohm or 1M input mode when it was damaged ?