Battery/Charge

I was driving today, noticed the voltmeter kept registering low voltage and my battery light would come on and go off. I though maybe belt, pulled into auto parts store, looked belt good, truck would not start. put new battery on, I have plenty of juice, buzzers, etc, but will not crank. Also even when key is off, buzzer goes off for few a short while. someone said may be ignition, another said starter, starter is relatively new, I have 89 GM Siera, K2500 5.7. I do not know what to do next, any ideas
:banghead:

you'd be surprised how a corroded ground can cause problems, check all minor as well as major ground points, battery to engine -engine to firewall- frame connection- battery to rad support. also if this doesn't fix it check the connections at starter ,a cable terminal may look good but if the wire looks green it may not be flowing enough amps through it