Sorry if this is asking the obvious, but have you checked between L+ and M to see if there is actually a 24V supply? Then you can try disconnecting all wires to the module except for L+ and M and see if the LED comes back on. Have you connected a computer to the PLC and checked in analog input word values i.e. AIW0.
After that you may be looking at a faulty analog unit or faulty PLC, or maybe the ribbon cable between the two.