Radio Problems!!!!!!

Hey guys
I have a slight problem with my factory radio/CD player...it doesn't work. I don't know what's wrong with it. All the wires are pluged in right and I can't find anywhere there are wires broken. But this is the wiredest thing. When the ignition is off the clock still stays and as well was the radio. Ok now this is where is gets even worse. When you press the button to make washer fluid come out it makes this static noise in the speakers and makes the clock and the radio dim down to nothing. If you press the heated mirror button it does thesame thing. Also when the car is off and now power is turned on anywhere if you hit the lever to turn the wipers on they come on. There are some strange things happneing with this car. So to sum up what the deal is when the car is off the radio and the clock stay on. Also while the car is off and while the radio is still on if you pres the heated mirror button or the washer fluid button you can hear static in the speakers. If you turn the wipers to the on postion they come on as well. This is all when the car is off. NOw when you turn the car on these things don't happen. There is no static. The other thing is even though the radio is pluger up right there is no sound. I don't know what too do and if you guys have any suggestions please let me know.
Thanks so much

TIm

[Aredubjay]

Tim,
I know this may sound wierd, but, check the wiring for the vanity mirrors in the sun visors. Pull the little plastic cover off the elbow on, first, the driver's side visor, use a small flat bladed screwdriver to pry the wires out of the channel and inspect them. If there are no broken wires there, try the passenger's side. I know it sounds totally unrelated, but, these vanity mirrors have caused all kinds of gremlins. If there are broken wires, tape up the ends to keep them from shorting.

You've got a short somewhere -- if it isn't in the visors, it may be in the stalk of your wipers (much harder to trace). You might also check under the hood to make sure you have a solid ground there (battery, alternator, etc.).

Those are the only things I can think of. Anyone else?