Occassionally my dash gauges and radio will loose power while my red battery indicating light will come. My dash lighting stays on. Also, if my headlights are on they will flicker from normal to brighter light. While this is happening my explorer is running fine. What gives? I replaced the original battery but the problem persists.

There are two things that could cause this problem. You either have a bad ground somewhere(like the grounding strap that goes from the engine to the frame, the one going from battery to frame, or something similer, or your alternator is going out. It sounds like the voltage regulator in the alternator is going out(will cause the computers to make the instruments do funky things)which would require alternator replacement. The difficult part of it, is unless it is doing it continuously, you won't be able to bench test the alternator and get reliable results. I suggest that you check the grounds, to rule them out, and look at a replacement alternator if that fails to fix the problem.

Yes, your problem remains in the alternator, also known as the generator wich alternates current to charge your batterry while accessories are on, eg, lights cd player and so forth, maybe a diode is losing the capability to handle the load, i recommend replacing the alternator or alternatively re-condition it. but that is most definately your problem.