What jgriffin means is that some head units will work without the key in the "accessory" position, other's will only have certain features work, like the eject button. What it means is that some head units will only work if they know that they key is in the ignition. The head unit knows this because after the key is in accessory, or the car is on, it receives a signal from the accessory wire telling it to come on.
Either the accessory lead that tells your radio to come on is dead (which would be really bad, since none of your radios will work anymore and you'll have to do some different wiring) or the head unit's reception of the signal is toast (which means the unit is bad and hopefully a new one will take care of the problem).
Of course, the best thing to do first would be to check all your fuses, including the ones under the hool for the accessories. If you have a Hayes manual, it will tell you which fuses are which.
Good luck,
Jon