If you don't have a multimeter get one. Then check the voltage between the white and the brown wire. It should be 12 Volt DC with the white wire negative and the brown wire positive.
The white wire would then go to the black wire on the propane
detector and the brown wire would go to the red wire on the propane
detector. As for the 2 blue wires, it would appear that the wire connections for the propane
detector were also used as connection points for something else. Try to determine what else isn't working.