OH DEAR! electric problems like this are never good! post any other info pls ( e.g does the headunit itself go off? is the amp going into protect mode or coming on and off? does it do it while driving and when stopped? when key is on first click? any headlight / indicator issues? or EW probs or weird dash behavior) as you probably suspect, there is no wire that connects the 2 at least there shouldnt be unless there is a serious electrical problem ( such as the loom is welding itself together!). First thing i would do is disconnect the amp totally, from the battery, earth and remote wire, and disconnect the connector block from the stereo or even better take the fuse out the fuse box. just to try to isolate the problem, its not worth burning the car down which by the sound of your problem could be highly possible. Be real careful thats all i can say at this time and if you smell any electrical burning smell, run!
