You should measure 3V (maybe something less). If there's no voltage you have a bad connection from the battery holder. If there's less than 2V it is possible that one of the 2 diodes (the one arrowed and the one close to it) is bad (one of those should essentially stop the board being juiced from the battery: if it's bad the battery juice all the board, even when switched off, and the battery goes low fast).
i've went to my mother's place during one of the school breaks quickly and had about 5 minutes to do some measurings - hope i didn't get any wrong results because of the hurry! well, the voltage measures for the battery came up with 0.91 volts

when you were talking about the 2 diodes which may be malefunctioning, i remember that someone else on the klov forum was already talking about this. i had posted a picture of the battery area because i had the feeling that there was still some corrosion / acid damage going on. have a look at the following picture


i did NOT remove any components from the board to get the following results:
- the resistor R26 which shows signs of acid damage is testing fine, however the one next to it (labeled R28 and circled in red) should give me a reading of 4700 Ohm with a tolerance of 10 % (yellow - purple - red - silver). i've measured that resistor multiple times now and it only gives me 3200 Ohm.
-then, i've measured the diodes D1 and D2 whose legs look somewhat corroded. this could be the reason why getting a reading of the measures is not always easy, sometimes it works, sometimes i have to move the multimeters tips around a little bit to make it work. D2 is fine, blocking the current in one direction and giving a reading of around 600 in the other. well, at least the video tutorials i've watched on youtube told me that those are good readings . D1 (circled in blue) however is also blocking the current in one direction, but gives me a negative reading of around -500 in the other direction. isn't the output always supposed to be positive?
you can find my old thread about this on KLOV
here!
i guess it would be a good idea to replace those diodes and resistors ...