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If the screen is not functioning, its light never comes on, or it simply shows nothing (not even under a bright direct light), then the LCD part of the remote has gone bad, in one way or another. The remote would have to be repaired, or replaced.
However, if it is less than 1 year from purchase date, and has not been treated badly, then it is covered by Logitech's warranty provisions, and it could be repaired by them under warranty terms for free. Let me know if that is the case, and I will advise you further.