HP 35s battery drain

[jebem]

This is a issue reported by several owners along the years on different internet forums.
Apparently there is no solution documented to fix it, except to ditch it and buy a new one.

It seems that the battery life is around 8 months when using it 1 hour per day, as seen on several seller's publications still easy to find by using Google search engine.

By searching this forum for this issue it is possible to find one comment by Katie Wasserman where she reports that a fresh set of batteries should last for around two and half years when leaving the calculator powered off.
This relatively short battery lifetime would be caused by a somewhat high standby current of 10 microampere, related to the power supply design and chip technology, and software routines used for deep sleep management.

I couldn't find any reports on failing capacitors causing this issue on this model.
However, surely a defective capacitor may cause excessive current consumption, and this model uses 3 electrolytic capacitors that are easy to replace.
Try using long life 105°C electrolytic caps from a new stock.
Old caps, even new in the box, can show signs of current leakage among other defects.

Measuring the current consumption in these cases would help, and it just requires a good multimeter, a external 3V battery holder or power supply, a pair of cables with oligators.

Other than that, there are quite a few SMD caps, resistors, and transistors, besides the two chips and the crystal/resonator.
Having the time and skills, all these components (except the two chips) can be replaced, starting with the ones connected to the two batteries power cables (that is the power supply section).

Eliminating all the above suspects, then a defective gate inside one of the two chips is the most probable cause, and it means a dead end imho.

Edit:
Look to Wikipedia for HP 35S. A nice internal view picture shows some details.