I encountered exactly the same issues with my old VL710. I wonder what the purpose is of the grease. After about nine years it finally became unrepairable. I've heard of people painting the underside of the buttons with conductive paint, but that too is a temporary fix.

I also have a VL600 that is starting to have the most-used buttons fail. When they do that it's time to give up the ghost.

These remotes are so inexpensive that it's easier to just replace them.