If you can manage to split the 5000T remote (and probably the 4000T), you can clean the rubber contacts which seem to get covered in grease of some kind (they should look dull, not shiny). I carefully rub them with a clean cotton bud. This usually returns the buttons to full operation for me.
There is a metallic film stuck to one half and I have had no problem with those contacts and so have not attempted to peel it off.
Splitting the remote is tricky, but possible (initially I dismissed it as impossible). I did it using one of the blades on a Swiss Army Knife (remember them?) sliding it carefully but firmly into the slim gap between the halves (but be very careful to avoid hurting your fingers).
Good luck.