I have a 92 civic vx hatch and when ever I have the radio connected the battery indicator comes on and the radio turns on and then off and the car starts to bogg. Also wen i am just idleing sometimes the battery light will come on and the car will idle funny almost as if it were stalling. when i turn on the lights it does this for a quick second too. i disconnected the battery while the car was running as an alternator check and it still ran. what shout i do??????

 

All those situations indicate low power... to me it sounds like the alternator is weak or there is a bad connection somewhere.
the ground from the engine to the frame would be my first target. (common problem)