M-audio av20 right speaker has no sound coming out of it at all...

To troubleshoot the problem start with the bit that is working - the left speaker.

1. Unplug the input leads on the back of the left speaker and swap them round.
2. If sound now comes out of right speaker and not the left the problem is with your sound source (computer, IPOD or whatever) or the connecting cable is faulty.
3. If there is still no sound from the right speaker try turning the volume control knob up and down quickly several times - does this produce any sound from the right speaker? Sometimes the electrical contacts get dirty and this can help clean them.
4. Turn the speakers off using the volume control knob. Disconnect the speaker wire for the right speaker from the OUTPUT on the left speaker (push the red and black tabs downwards and gently pull the wires out. Find a small 1.5 volt battery (an AA or AAA size will do nicely) and touch the bare ends of the speaker wire briefly on the battery terminals. If you hear a slight crackling sound the wire and the speaker are okay and the problem is in the amplifier, which will need repair or replacement - not a job for an amateur.
5. If you don't get any sound from the battery test find another piece of speaker wire (any piece of 2 core cable with bare ends will do for testing) and repeat the battery test. If you get sound then replace the speaker wire. If not remove the speaker wire again and go to next step.
6. Lay the speaker face downwards and carefully unscrew the back panel (don't do this if it is still under manufacturers warranty - take it back for repair or replacement). Lift the back panel off carefully and slowly taking care not to pull the connecting wires inside the cabinet, which will probably be quite short. You may have to settle for just rotating the back panel slightly so that you can see inside if the wires are too short to do otherwise.
7. Use sticky tape to tightly attach the bare ends of the speaker wires to the terminals of the battery. Touch the loose ends of the speaker wires on the two metal terminals where the internal wires are joined onto the back of the big loudspeaker cone. If this produces a crackling sound it is the internal wiring in the cabinet that needs re-soldering. Otherwise the loudspeaker unit has failed and will need replacement.