This is the more recurrent problem I have found so far. Four units I have fixed, included my own one, had related problems. And, in all cases, battery voltage was fine, but it had leaked.
Problems caused by this are mostly related to the display, from a completely dark one to a semi-working one, but you can get all kind of weird problems, as data and control lines from the main CPU pass just below the battery.
The problem is that the battery side you see is the good one. I mean, it is the one which is all metal so leak happens just in the opposite side. But you can have a hint if there is some gold-colored spots.
Here you have some pictures of three different units with same problem. Unit #1 so far was the worst damaged, as it needed some other side wires to fix it:
As you can see, in all cases I installed a battery socket for the more common CR-2032 (classic PC backup battery), so next time replacement will be easier.
There is lots more info on the repair of the TS-790 #1, as it is my own unit :-). It took some work to fix, as you can read at my BLOG: