It's pretty rare, but certainly not impossible, for the LEDs to have gone bad. Far more likely that one of the ICs in the remote has gone out, probably an LED driver board or similar.
Best bet if you want to stick with the 880 and not reprogram is to look for used ones on eBay. They're old enough now they can be had cheaply, especially if you're willing to take yours apart and cobble together a working unit from a couple of non-working. Good time to build up some spares. That's what I did before moving on from Harmony. I was able to keep my batch running for years that way.
As far as copying your programming, only going to be possible with a like model. You should be able to plug it and download to another 880, an 890, or an 880/890 pro. Going with any of the newer models, even the now discontinued 900, requires reprogramming.