1979 Pontiac Firebird My 1979 Firebird makes buzzing noise

My 1979 Firebird started making a buzzing noise coming from the passenger side of the car (it sounds like its coming from the back of the engine compartment). It started while the car was running and when I got to work I turned the car and ignition off. The buzzing stopped. Turn the key to 'on' and the buzzing starts again, I try to start, and nothing, the starter might give a weak grunt but then nothing(it is as if the battery was dead). The buzzing continues loudly the whole time the ignition is 'on'. I had plenty of power too. I had a spare battery that I was carrying with me and I also tried jump starting using a running vehicle. I was watching the voltage gauge on the dash and it registered that there was plenty of power. Thanks in advance!


Edit
Ok, so the above happened at about 6 am this morning, It is now 11 am, Turned the ignition on and nothing, so I went out and reseated the battery cable and tried to start the car. The car started right up, but its still making the loud humming/buzz/vibrating noise coming from passanger side of the car. It sounds like if you but an electric razor or a vibrator on the hood of the car. Its a 35 mile drive home. Is it safe to drive it that far? Still wondering what might be causing this issue. Thanks in advance.