For anyone reading this in 2022, the posts above in this thread are from 2016 to 2019, and the operating voltage and other electrical specification have changed with the Mayfly boards released in the past year. The older Mayfly v0.5 boards had completely different input voltage limits compared to the new Mayfly v1.0 and v1.1 boards. So the advice above about connecting 12v batteries directly to the Mayfly is not applicable to the new boards.
For v0.5b, LED3 should only be on if the mosfet transistor on the Mayfly is turned on, which should only happen if you set pin D22 to high in order to turn on the switched sensor output power circuit. If yours is on all the time, or partway, then either that mosfet is electrically damaged, or there’s something wrong with another part of the board. Since you’re saying the onboard ADC is not always right, then my guess is that you’ve got a tiny bit of corrosion somewhere on the board (probably around the main processor chip in the center) that’s causing noisy input to the analog ADC input pin, and also causing D22 to appear high, triggering the mosfet. Has your board been subjected to high humidity and/or condensation? Or ants? We had a station start malfunctioning after a few tiny ants made their home in the logger box and laid some eggs on the circuit board, resulting in corrosion and failure of the Mayfly after just a few days.
And if you’re still using a Digi LTE module with EnviroDIY LTEBee adapter, that could be contributing to the odd behavior as we saw lots of random failures of those due to a still-unresolved issue with the Digi boards, which is why we stopped using those cell modules and designed our own. Have you tried removing all sensors, the solar panel, any external power sources, and the cell board and just operate the station with nothing attached but a lipo battery and/or a USB cable to see if it operates normally and records data to a card?