There are two CIA chips in every Amiga. These handle most of the Amigas communication to the outside world- the serial, parallel, joystick, and mouse ports, as well as the disk drive, keyboard, and timer. If the CIA chips become damaged you may develop problems with these ports that may manifest themselves in a number of ways. These include broken fire buttons on the joystick, disks not being recognised, or the keyboard not recognising presses.
Fortunately, these chips are easy to replace, At least, they are on the A500 and A2000. To see if this is the problem try swapping the two CIA's around to see if one of them is faulty. This may temporarily allow a certain port that you use to work. However, this is only a short term solution and you should replace the CIA chips with new ones at the earliest opportunity. These retail for around £10-20.
To swap the CIA chips you will need to take the Amigas case off and remove the metal shielding underneath. The two CIA's are both 40-pin chips that are marked CIA ODD and CIA EVEN. Simply swap them over, making sure that you have placed them in the right way and replace the case.