It sounds like your speakers are dead. It is one thing to diagnose a sound problem when the power is on and no sound comes through, but if the power is off, not a good sign.
You can try things like leaving it off for awhile and re-plugging it in, or other things, but unless the power light comes on, it is dead.
But seriously, computer speakers are cheap unless you have a giant surround sound system. IMO, I would just replace them.