Trouble Shooting Nightmare

Car: 2003 Toyota Corolla S System Specs: Pioneer DEH-P850MP 6-1/2 Diamond Audio M6 series Components in front doors Kenwood KFC-X698 6x9's in back deck 1 Kicker amp 800.2 1 Kicker amp 600.4 1 12" L5 Kicker Sub 1 Farad PG Cap Got this installed at a local audio shop. I heard a "static type" noise in the speakers once in awhile. It is hard to put into words. It would happen once in awhile. I thought it may be the CD so I switched CDs and the same problem occured. This problem is intermittent. Does it at high and low volumns. That's not the main problem. The other problem is my system would shut down. Almost like it is going into safe mode from the amps overheating. However, I felt both amps when it shut down and they were fine. The power was also on the head unit, and both amps. To start to narrow the problem down the audio place thought it may be the head unit. Since the amps weren't actually shutting down they thought the head unit may be bad. So, they swapped it out with another head unit. The problem is still happening. To continue trouble shooting we thought the head unit was not working right when it was at high volumn. The head unit was tuned at about 53 and it maxes out at 60. So, they turned the gains up on the amps and the head unit was tuned around 45. Well, the problem is still happening. The system will shut down for approx. 10 seconds and come back on. I also hear the static noise. I am not sure if the static and shut down is within the same problem. To point out the common factors is it possible the remote wire is bad in some way? Since both amps are shutting down? I am taking it back to the shop this Sat. of course the problem will bot reproduce for them to trouble shoot properly. Like I said it is only happening once in awhile and I think it is something with the wiring. Any ideas would be greatly appreciated!"It ain't loud enough until your heart skips a beat"

well if the amps are staying on, and the subs and speakers are cutting out...plus you have a funny noise coming thru the speakers, that leads me to believe there is a problem with the RCA's.   maybe they are pinched or are ran improperly and that is causing them to pick up noise thru the speakers.  but its hard to tell without seeing it...but just based on what you wrote, i would tell the shop to check out the RCA's.