Just call Harmony but don't explain that the LCD is broken, just say it stopped working, they may or may not ask you to send it in. (I find it's 50/50 with them) anyway when they get it, they will have already generated a replace order and just send you out a new one. Trust me the guy in charge of sending you a new one just cares that you sent him the defective one and could care less why or how the LCD does not work.
I had many many issues with my Harmony 880's and they wound up sending me out three free replacements just because I said it wouldn't charge and only one time did they ask for the charging bass (not even the remote) and they sent me an entire 880 unit, So i jury rigged the non charging remote to finally charge and I would just charge it on the new unit and use in spare bedroom and when the battery would get low, I would take it to the new base and charge and reuse it. But that series of remote became so frustrating with charging, I wound up just giving away all three of my 880's and going back to the 659's (which Harmony sold me at half price for4 all three years after my warranty ended, because I was so displeased with the remotres. My 659's have worked flawlessly.