Horn do not want to sound on a mitsubish lancer 2002

Sounds like the horn relay is bad, the fuse for the horn is located on the driver side look under the left of the steering wheel you will see a little compartment pull it out and you will see the fuses.

I would check for the following:
1. Fuse
2. Relay
3. Wiring
4. Horn itself (disconnect it from the car, use a wire to connect to horn and tap it directly to the battery, if it horns then it is ok, if not probably need a replacement.
5. Push button on the steering wheel
6. Rotor contact on the steering wheel

check the horn relay in the engine bay relay compartment .It might be sticking on. Maybe swap the relay and see if fault moves to other device.

sounds like there's a short in your wiring in the steering column, A lot of times with a tilt wheel a wire get loose or gets a short in it. the steering wheel may have to come off to fix the problem but make sure to disconnect the airbag first, I'm not sure what vehicle you have so I don't know where to tell you to look for the connection, may be best to take to a dealership if possible. Hope this helps.

have to remove airbag to fix this

take the wire off the battery that goes to the alarm.

I hate to point out the obvious - but are you sure it is a 4g13 engine? That is mitsubishi's 1.3l engine. Your profile has no info saying what country you are from - but I think all 2005 mitsubish lancer engines will be >1.3L
There is a 4g93 1.8l dohc engine.

computer problem by the sound of it ??if it is then its dealer only

Have you checked the fuse r the connections at the horn it self that is under the hood

there is a wire that runs up the center of tour streeing column and plugs into the back of the horn switch, it is possible one of these wires has come off