it probably doesn't help but my key fob stopped unlocking and locking my 2011 LR 4 out of the blue. same thing, I could start it by putting it under the steering column. took it to the dealer they replaced the battery for free and tested the remote( turns out the remote was fine) it was something with the car not processing the signal or some BS. told me $230per hour but they think its what ever controls the locks( sounded expen$ive) so I opted to go home and google. on my drive home the air suspension shut off along with a plethora of warning lights. long story short it was because my alignment was out.... I kid you not. I jumped under with a wrench and turned out the tie rod ends till the steering wheel was perfectly centered again( getting new tires the next week so didn't care that the alignment was all messed up) and instantly everything was back to normal... even the locking and unlocking. i dont know if this will apply to you because my car was still drivable but good luck.