Check to make sure both CIA chips are seated, in fact check all the socketed chips to make sure they are pushed all the way down (without putting too much pressure on the motherboard to damage it). If all chips are seated well, replace the CIA chips with new ones, one at a time with a test in between each replacement, so you can narrow down which CIA chip has gone bad, if indeed that is the problem. I would have also suggested that there is a fuse on most Amigas that protects the mouse/joystick ports, but I am guessing that the fuse is still good since you are getting menus when the right mouse button is pushed down.
Another possible problem would be the mouse port pins. One of them could be broken off and missing.
