Here is an update where now it seems clear what board is in partial fail.
As a reminder, I have two TDS540C where the healthy one has 2GS/s standard and the partial failed one 1GS/s.
I've deconstructed each acquisition board then I've swapped these boards. From the attached picture, we can now verify that the FAIL ++Processor is ONLY due to acquisition board.
Not sure if this can help but here is both boards with their memories chip.
TDS540C-1G failed Serial B010811
Processor board S/N 9740L
DS1486-120 9735H
DS1650Y-100 9716U
flashfile E28F016SA
Firmware V5.0.1e
Acquisition board S/N 9745D
EEPROM X24C02
TDS540C-2G working Serial B010489
Processor board S/N 9724A
DS1486-120 9723H
DS1650Y-100 9650H
flashfile E28F016SA
Firmware V5.0e
Acquisition board S/N 9810G
EEPROM X24C02
As a reminder, it was previously dumped the correct NVRAM content from the healthy one to the failed one but this did not solve the failure. This is why I decided to swap acquisition boards in order to estimate what sub-system is failed. This TDS540C has also one knob of its front panel partially failed
https://www.eevblog.com/forum/repair/tds-540c-partial-failure-horizontal-scale/ so I guess best to keep it for spare parts.
Unless one knows exactly what is wrong on the acquisition board (i.e. X24C02 EEPROM), my understanding whatever I do with this TDS, it will have to go into a full calibration FAS which I've never done so far. Time is money so maybe best I keep this TDS540C with spare parts in case the other fails one day.
On a side note, I wonder if one possible explanation is not linked to the fact the healthy TDS540C Acquisition board S/N dates 1998 even though the failed TDS540C is younger.
About the NVRAMs, I'm ware these are quite old circa 1996 and 1997 implying their potted batteries might fail in the near future so I'm dumping-saving the content of these NVRAMs as well as its flashfile firmware and EEPROM just in case. There seems to be different options to secure or replace the NVRAM chip (1486 and 1650Y) so I need to study and decide what is best in the long term.
Any idea, comment, suggestion... thank you in advance