You need to replace the main/board for sure located in the lower rear left hand wall of the unit in a plastic case, it will have 3 wire harnesses unplug the unit,undo the plastic container and unplug the the board and there will be a burned spot on the case and burned trace on the circuit board, reason being,this is very common on any of these sideXsides,if a light blows out in the refrige compartment it puts a surge on the board and burns the circuit trace open,this makes the digital temp read-out go dark and if the lamps light at all they "strobe" dimly or not at all,and you will hear a clicking of the relays in the rear area trying to latch the light bulb circuitry, but cant because the main/mother-board is defective now

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This is a common control board failure that FixYourBoard.com can repair
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W10135090 Whirlpool ELECTRONIC CONTROL BOARD MAIN CIRCUIT BOARD