Sorry for asking for confirmation, I just wanted to absolutely certain that the remote wasn't a contributing factor. The bad news, as you seem to have concluded, is that something about the TV, possibly the software update, is the problem. And it's out of warranty, being two years old. I was wanting to be sure it wasn't something simple. And it's not.
If it's a physical issue with the Roku TV, then you would need to follow through with the manufacturer.
I have seen that some have been able to force a better update via a USB as described on the page How to use USB to update your Roku TV.
This last thing isn't often the way to go, but it should be ruled out, just in case. Sometimes the update from your network is problematic. It happens. So update from a different network. Use your phone's hotspot to connect your Roku TV, then do a full factory reset, via menu if possible, or pressing the reset button/pinhole for a continuous 30 seconds (a full 30 seconds). Then connect to your hotspot for the update.
Roku Community Streaming Expert
Note: I am not a Roku employee.
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