HP 41C / issue to turn it on

[Frido Bohn]

To me it sounds to be a more complex issue than just messy contacts of the keyboard. The malfunction may be linked to the infamous zebra-strip contact between keyboard layer and circuit board which is related to the broken-post problem (transport damage?). You may have a quick check if you press firmly on the area between <ON/USER> <PRGM/ALPHA> and the first row of keys while attempting to switch on the calculator as per user manual.
Maybe the problem is even more complex and is related to a damaged circuit board. Radiation at flight checks seems to be a remote cause: consider that the HP41 was used in the Space Shuttle program because its insensibility due to radiation. Consider also that the seller was not that truthful.

Cheers
Frido