While it's not impossible, it is unlikely that the LED is burnt out.
What's more likely is that the LED has become disengaged from the cup holder (the LED is on when ambient is on, but is not projecting through to where it can be seen) Or...
The connector has come apart (disconnected) beneath the cup holder.
Either way, a partial console lift is needed to investigate. If the warranty is finished, it's a super-simple job. If the warranty is still in effect...
Please follow up in order to help others (although it does appear that there aren't any, doesn't it?)
It's in warranty but I'm not overly keen on letting the dealer loose on the interior trim. Might have to bite the bullet and risk taking it in. There are a few other warranty issue to get done at the same time.
I completely agree re: letting the stealer have his way with your ride. I cannot STAND taking my car in!! And so...
Honestly - I would have a peek myself IIWY. It's super-simple to lift the back end of the console up a bit to see if you can see the light shining under there (or trace the wire with your finger to see if it has come undone) If you can deal with it yourself, that's one less thing for the stealer to screw up.