i’ll be honest, i have no idea what the problem is … my WDTV Media Player and Remote works fine.
Dunno, maybe try a plugging in a USB Keyboard and see if it does the same thing ?
or even via the WEB UI or the Android App.
If all the above work ok, then i guess it could be the remote ? … but, you need to test the other ways, before confirming that.
(ps. no-one else in the house possibly playing a prank on you ? … because what you describe, is Very Odd Behaviour)