Paula only handles the right mouse button, and that has never been a problem on any of the repairs I have done to an Amiga ever since I started working on Amigas back in 1987.
The mouse port on an A2000 has a fuse, and that's the prime suspect (green wired part, looks almost like a resistor and can be bridged with a thin wire). After that, you check the LS157 multiplexer for mouse directions and the CIA chips for left mouse button. Very low-cost parts, easy to exchange on an A2000.
Thank you. And your are right, the two buttons are working, the movement is not working. Will check the fuse and U202/LS157.