crackling sound through speakers, dome l

Okay so i have an electrical problem that i cant seem to get to the bottom of. upon starting the car, there is a popping noice that goes through the speakers and the dash lights flicker on and then off. voltage reading with the car running is somewhere around 12.2-12.6, obviously way to low. with the car off and the key turned back, there is no power to anything, radio doesnt turn on, dome lights, windows, nothing. when locking the car the normal beep of the horn is very subtle, sounds like its muffled. headlights flicker when any high current is used(ie. power windows). dome lights flicker on and off with a clicking noise coming from the lower left kick panel, near the fuse panel....sorry for the long post but i just wanted to give all the symptoms so someone could possibly help me out. battery is brand new so it cant be that, i would think it would be the alternator but that shouldnt have any when the car isnt running correct?? thanks in advance, chad