I thought I'd give a final update on the repair of LC584AL:
After I found out the overload protection circuit is at fault and extracted the schematics (see post #19) I could not explain how that circuit could protect anything!
If the double diodes are perfectly matched, any change in temperature would not trip the opamp (their sum voltage remains zero). Anyways, I went ahead and simulated this circuit in NI Multisim (I have access to at work) and still could not figure how this thing can protect again overheating of the 300 ohm resistor. I think this thing does not protect against anything unless there is some mismatch, but not too much of it, between the diodes.
If they are mismatched by a lot the opamp trips at room temp which is what has happened to my scope I guess and if they are perfectly matched then nothing will happen with temperature. In LC574 there was a potentiometer to adjust this circuit but it is eliminated in LC584. Besides, even if it were to work as intended, it would take a while for the over-voltage at input to warm up the 300ohm resistor enough so the diodes voltage difference can trip the opamp. By that time the damage is probably done. So the ability of this circuit to protect the input is very low (none). And it only works at 50Ohm coupling, however, if it trips, the input becomes disconnected and does not work on 1M either until the overload is cleared.
So the solution for me was to just DISABLE this subcircuit instead of going through the painful and expensive job of removing the silicone putting and replacing the diode and re-applying the silicone. The easiest and cleanest way to do this was to just remove the 4.7K resistor (R4081 at the output of AD705 on the back of the mainboard). This way the output of LM339 comparator remains high and the input relay will not disconnect the port anymore. At the same time I have not changed the biasing conditions of any of opamp/comparator pins. So this repair costs nothing!
I did this and the scope works like a charm. All 4 channels work perfectly and I wish I had done the same on other channels when it was open.
I borrowed a GPIB cable from work and updated the firmware to 9.3 (last version) and some of the bugs I had noticed in operation are now gone.
The scope has so many software options and looks pretty much brand new :-)
The floppy also works!
thanks for your comments and help.