I have the same problem with TZ40. As Peter has already written, the reason for this strange phenomenon is that the video button is connected to the same resistor chain as the zoom lever switch. In TZ40 it is possible to zoom using the “buttons” on the display. This, of course, is not as handy as using the lever, but it does not start video recording. I do not know if this is possible in ZS25.
I also tried the trick Saul presented, and it seems to work in my camera as well. It is a bit difficult to understand why, but does it matter…
in my DMC-TZ40 I had the same symptom. Blowing seemed to be some kind of temporary solution. I am not sure about the mechanism, maybe it somehow makes some switch connections better for a time. The actual reason of the problem is the way the moving of the zoom ring and video recording are detected in the camera. It is analogue. There is a chain of resistors in the camera. One end of the chain is earthed. Apparently a constant current is fed to the chain, and the voltage in the not-eathed end of the chain is sensed. Turning the zoom ring or pushing the video button connects a different point in the resistor chain to earth. This solution makes the mechanical construction easy. Via only one connection to an IC the position of zoom ring and pushing of video button can be sensed. I got a solution to the problem by buying the PCB where the contacts and resistors are placed, and replacing the faulty unit. The PCB had name Top P.C.B. It was not very easy to purchase the unit, to say nothing of replacing it. But now the camera works again.