Hi remember no need to cross post between forums for help.
Want to ask as some had fuse " fuse that was known to cause HC power etc issues.
However garbled display is not usually a symptom of a bad F2.?? It could be (usual culprits):
The CPU, only test by replacement, or feel if CPU is hot?
The EPROM, again test by replacement
The Displays themselves, The First display (LHS) overflows data to the 2nd RH display a bad first (LH) display can cause garbled issues.?? Test by swapping HC LH display t the RH position and the RH to the LH position.?? or
The HC itself could be the issue aka a bad U4 buffer IC.
All that said it is unusual to have garbled display and also power failure in the HC as generally they are separate things ...the only commonality is +5V being lost to the HC.?? The HC LED is actually powered from 5.4V.? Indeed you said the HC button presses would not respond so this again takes me back to possible loss of +5V to the HC.? Maybe a bad HC cable or corrosion around the HC cable socket.
So what I have given you is a starting point to look at the 5V and a few other things to look at and try.?? Get back if you need more help
regards
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Brendan