The HDR-2000T official remote can be fascinating for how short a life it can have.
My HDR-2000T is with someone as their only recorder, and what we settled on is a remote from Humax Direct usually sold as a remote for HDR-1800T. the Humax RM-H06S. https://www.humaxdirect.co.uk/accessories/rm-h06s.html
We tried a couple of alternative sources for a new genuine Humax RM-H06S, which when I placed my orders I thought were the original article, but they were both a waste of time.
The RM-H06S can be used to control slightly more of your HDR-2000T than the normal HDR-2000T remote but lacks the ability to control any TVs directly. I.e. it has no TV mode toggle button, and because of this you would still need to have your TV remote to hand.