I have Sony remote controls that don't have screws or the opening holes at the back. The top (button side) is clipped to the bottom and has overhanging lips that cover the seam on the sides. These can be opened with a thin flat blade (such as a decorators scraper). Turn the remote so the buttons face downwards and gently slide the blade downwards under the side lip half way along the side of the remote and then gently work along that side to both ends to release all catches on that side. Repeat on the other side.
Then clean the contacts on the circuit board and the rubber buttons with contact cleaner. I've found glass cleaner and cleaning alcohol also work