The operating voltage is obviously not reaching the other electronics in the camera as
@Henning Serger assumes. The two battery contacts in the battery compartment into which the second battery holder is inserted could be the problem here. I would work on these intensively with electronic cleaner and an eraser.
I would definitely check the output voltage on both battery holders with a multimeter, it should be at least 2 x 4.5 volts with fresh batteries. If it is less or 0 volts, a contact problem could be the cause - clean as described above.
If that doesn't help, the camera must be opened to check whether voltage can be measured at the inputs on the circuit board for the operating voltage. However, disassembling the F4 is not trivial.
From then on it becomes difficult to check because you need to know the circuit to do so. The troubleshooting tips in the service manual or SPT journal for the F4 may help. But that is already very special.
It is interesting that both F4s show the same error after a long period of inactivity. Nothing should actually break on its own there, so I suspect a problem with the power supply/contacts by (invisible) oxidation.