Hi,
Recently I managed to acquire an other 5340A in half working condition, thanks eBay.
This new unit is really dirty and not in the same nice shape as the other one but it will help me to advance in the repair process.





The interesting thing is that the device is equipped with a quite rare option for this counter, the GPIB interface

After another session of card swapping, I was able to confirm my doubts about the faulty Command Board (A21).
Using the board from the new device made the old device counting again

The responsible of the faulty board is the 1816-0003.
This CI is a PROM and after some investigation I found in a old HP catalogue that the equivalent references are : 74S188, 54S188, DM8022

The content of the PROM is available in thee Service Documentation.
Now I have to find a way to program this PROM, I do not have any clue how to do that (first time I have to deal with a PROM)