Typical Problems with M-Audio AV40 speakers:

*** My conclusion is that the power supply circuitry's design is the cause of failure of these speakers in most cases.  More specifically, the power supply filter circuitry on the main board in the right speaker heats up too much!  This causes the capacitors to start to fail that expose the issue as units that don't turn on, have noisy sound since the capacitors have lost their useful life to filter out power noise, or no sound in one speaker since one of the internal connectors for audio signal is close to the overheating power supply ***

Type 1 Problem: Both speakers just die after a while and do not turn on:

The most likely cause besides the obvious (bad power cord, etc): the power supply capacitors may have gone bad and would need to be replaced.  You can physically diagnose this in most cases by opening the left speaker and looking at the internal power supply circuitry and looking for bodges in them.  There are four capacitor for the power supply and they are larger than the others toward the corner of the board near the 3-wire plastic connector header that come from the transformer inside the box.  You may also see some signs of over heating around the capacitors in forms of darkened circuit board, etc.  The cause of this problem is that by design the two large blue power resistors that are standing off of the board next to the capacitors along with the zener diodes that are next to them tend to pass quite a bit of current and are supposed to heat up.  However, besides the ambient air-cooling in the enclosure, there isn't much to cool them down.  The electrolytic capacitors loose significant of their useful life when operated in overheated conditions, which results in them breaking down in these speakers sooner than expected for a consumer electronic. You can read the value and voltage reading of the capacitor and replace them to fix the most power supply issues. Capacitors are about $1-$2 at RadioShack or even online at Amazon (see 220uf 25V capacitors on Amazon)

Type 2 Problem: There is a humming noise coming from the speakers:

Type 3 Problem: There is not any or there is only bass in one speaker:

Type 4 Problem: There is only sound coming from one speaker (typically the left one):

More on the troubleshooting that I did: I did not remove any of the internal header contacts or take any of the internal wiring apart since I was trying to maintain the original integrity and hot glues that were holding things together.  The way the circuitry in the left speaker works is that the signal from the audio inputs get pre-amplified on the main board.  Then they go to a header and with a set of the internal wires off of that board (may be to the volume nub in that speaker) and then back to the main board.  A similar thing happens at the inputs for the final Power Audio Amplifier.  If the wires/connectors are not the issue, I drafted the circuitry from what I saw as following.  Since the right and left channel circuitry are symmetrical, you can use an oscilloscope or a DMM (power/AC mode) to see where in one channel the signal is getting lost.  Note that for this diagnostic, you will need to have the circuit board powered up (WARNING: YOU NEED TO KNOW WHAT YOU ARE DOING SINCE IF YOU TOUCH THE A 110v/220v BARE WIRE, YOU CAN DIE).

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