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I don't know if you mean the LCD trip below the speedo or the actual LED in the triple pod on the dash. I'm just clarifying because I know people that use LED & LCD interchangeably.
In any case...I've never known either to go bad, and it's certainly not something I want to have to deal with, I put in my hours fixing my HUD speedo on my 240SX - I'm done with that!
I spent a little while going over some stuff in the factory service manual and I didn't see any "fixes" for either one, my guess is that it's just a part will have to get swapped out.
Here's a link to the correct chapter in the FSM if you want to look around:
2004 350Z FSM - Driver Information System.
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