Elusive stereo problem in 2005 Camry

I have an 05 camry with JBL and nav, it's one of the older in-dash processors which has fortunately been phased out of the Camry (edited in light of Tideland Prius's post). When you first start the car, it sounds fine, but after you've been driving for about 8 to 12 minutes, a click is heard through the speakers whether or not the audio system is on. From this click henceforth, any sound coming through the speakers is converted to a harsh, unpleasant fuzz. Bass creates a scratchy artifact, midrange is all fuzz, and oddly enough, soprano voice sounds completely fine. The radio, cd player, navigation voice, and even beeps are effected, and electrical noise comes through the speakers even when the audio system is off (leading me to think that the headunit is not involved). Restart the car and the problem immediately goes away. It does this 99.999% of the times you drive the car, one of the rare exceptions was of course when we brought it to the dealer. It only happens if the car has been driven since the last power-up, but will do it standing still. My mother left it idling for 20 minutes once (talk about a waste of gas!) and it didn't do it. It started doing this about 6 months ago when the car was at 70,000 miles, and I'm coming up on 94,000 and it still has not been fixed, which leads me too...

The lovely toyota dealer experience!

The first time we told them about it at a regular service, they said they'd check it out, which of course they didn't do.

At the next service, we described the conditions under which it occurs, and they said they'd listen for it. When we got it back, he said he left the cd player on the entire time he worked on it and it never did it. GGGRRRR! We didn't JUST tell him that it only ever happened when the car was DRIVEN!

At the next service, they said they'd take it for a spin and listen, but the deaf bloke claimed he couldn't hear it.

At the NEXT service, we happened to get a dealer with an intact auditory cortex, but perhaps damage to [most] other parts of his brain. I popped in a pipe organ CD (the type of music effected the worst), and this time he heard it, but INSISTED that the speakers where blown. We calmly asked him why it sounded ok for the last 10 minutes. He was overwhelmed. He grabbed another dealer, who had a listen and also heard it. This dumb-dumb told us that in order to fix it they'd have to replace the entire headunit and Amp. My mother asked if they could do some diagnosting testing and try to locate the problem. He said "yes, but it would cost a lot. We'd have to rip all the door panels off and everything". She asked "why would you have to do that if the problem's in the headunit and amp". "because the speakers might be blown"... His conclusion was that "we don't deal with navigation systems" (funny considering the screen is emblazoned with "toyota"), and he offered no insight as to where to go for this problem, other than to replace the headunit, amp, and speakers.

AAArrgh! Has anyone had this problem with their stereo? or this problem with their dealers?