You probably know this, but, a joystick (if plugged into port 1) wont control the workbench pointer like a functional mouse would. The fact that port 2 works with a joystick is a good sign for the ports.
Mice (mouses) are notoriously unreliable. The original Amiga mouse has a ball that turns 2 shafts (x and y axis). Cleaning doesn't always work. Try removing the ball and turning the shafts with your finger, this is easier if you disassemble the mouse. If this works, a new mouse is the way to go.
