TV has sound but screen is black.

You are using composite cables(red,white,yellow) mine did the same thing. The aquos is all digital, wont read analog, which is what composite cables are.
They now make a component cable for the wii. I paid $28 at b.b.

The tv was working fine until this morning, then the picture went out but the sound is still working.
TV is only 3 years old, no real electrical problems

All old DLP tvs have a common design flaw,any time this could happen during the tv existing life,the tv problems is call a convergence problems,it dead.Tv have colors lines R,G,B mis alignments,have colors shadows pictures or 3D pictures look alike?The tv convergence board is dead,the board have dead 2 STK convergence ICS and some or all of it resistors too.This parts on the tv convergence board,must me replaced,to solved the tv picture convergence problems.The shop,will cost u like $300-350 for parts and labors.

There is a fuse in tvs I've had to change one myself

Turn off TV. Turn on TV, use remote to turn off SAP. Now I have sound on all stations.

turn power switch on in the back. red light on in the front, hold the power button until system turns back off. this resets all hardware settings. if this doesn't work and the system is ok (green light) then you have a connection problem to the tv

the vertical drive ic that drives the yoke for vertical sweep has blown.
sometimes it is solder problems like sharp and toshiba had.
the part is 10$ the pc board will label it ,the yoke is the coil setup on the picture tube.if you follow the wiring half goes to the horizontal drive,and the others to the vertical section.the chip drives the coil directly.there are VERY high voltages in there ,even turned off. the pix tube cap on top is 30000v. like a stun gun.the horizontal drive 2000 volts and the main power supply 165 volts dc high current.you need a special setup to discharge the picture tube.

I have a Mitsubishi  "CS-3515R.  Serial number 528801. When I turn it on by remote or on the set itself, I can hear the power come on.  BUT there is no picture and no sound.  What do I do?

thanks for your detailed description of what happened.
replacing the vertical output i.c will correct the problem.
the reason it failed was bad connections on it.

Did you have color problems in past? Most of these sets have convergence problems. Amps goes out. But you should have seen some type of distortion from color, red,blue, green. If no color problems then maybe vertical ouput out or horizontal output bad.