I would start by probing those test points marked with T4, T7 and T8. T5 looks like GND. If that chip is an LW24C02 its an EEPROM. It is probably used for storing the mode (g and oz) an the zero.
T4 may have an interesting value since it come from the "chip on blob" which is surely the LCD driver.
Where does the white and blue wire go? They also look interesting. Are there any other chips on that board?