To clarify the problem that my friend and I had.

When the problem occurred, the voltage level across the whole car was dropping. You could see this from the fact that the internal courtesy light would dim, the headlights were not as bright as they should be, the instrument illumination would almost go out, as would the tail lights.

As Tony says, though, it could simply be the wiring to the headunit itself. The sure way to tell is to measure the voltage directly across the battery terminals when the electrical system is under maximum load (e.g. air-con, full beam headlights etc.). If it drops below about 12 volts (should be 14.8 with no load), then I would have to suspect either the battery or the alternator.

If the voltage drop is only on the wiring for the headunit inside the car, then it's likely to be this wiring that is somehow causing the problem.

Andy.