On the later model Amiga 2000 systems this is
usually due to a blown fuse, F1, on the A2000 motherboard,
though the port controller chip is also a possibility;
early A2000 revisions did not have the fuse, so
the chip is definitely the source of failure. For
other models, it may be a similar fuse if such
exists, or the port controller chip. Static can
blow the fuse or chip, but an attempt to use an
incorrectly wired GPI cable on the joystick port
is another common cause.
On those models with a fuse, the fuse must be
replaced, and is a soldered-in component that looks
like a resistor, but is green in color. The component
is located right behind the mouse and joystick
ports. You will most likely wish to have a service
center do the repair.
Depending on the Amiga model, the port controller
chip may be either socketed or surface mount. "Paula" is
the major chip associated with the mouse/joy ports,
but there are driver chips in the circuit as well,
which vary depending on the model.
Again, it may be safest to refer to an Amiga service
center for diagnostics and repair.