Detecting state of a button when in parallel with LED
First you have to know how the switch is wired. You can open it to check what is inside, or guess through measurements. It could be like this, this schematic shows several possibilities.





The button could be across the LED (wire labeled 2 on schematic) or across a LED+resistor in series (labeled 1) and there could be a resistor R2 in series with the whole thing, or maybe not.

To investigate this, don't use a ohmmeter as this will give bogus measurements across a diode like a LED. Instead you can power the switch from a +12V or +5V power supply with a resistor in series (say, 1k). Then measure voltage across the switch when the button is not pressed, and when the button is pressed.

When the button is not pressed you'll have a LED in series with a resistor, so by using two supply voltages (+12 and +5) and knowing the LED color (thus its forward voltage) you can determine the series resistor value. Then when pressing the button and measuring the voltage across the switch, you can determine how the button is wired. If foltage drops ot near zero then it will be option "1" in schematic above and no R2.

After you do this you can determine whether you'll need to use ADC to sample your voltage. The ideal solution would be to have a clearly defined logic level, but that will depend on the way the switch is wired. So, please update the question when you have more info.