a few possibilities here..

bad battery, or bad ignition (start) circuit..

if the battery has 12v, it might not have the amps if the plates have fused together, you should go get one the free free tests done, or hook up a jump and see if your problem goes away. both of those could point out the battery.

if the battery is ok, then the system is not putting the power out when the ignition is in start. this could be relays, fuses, wires or the starter.. even the ignition switch, once you have proven the battery, test everything in the "run" position without starting the car, then put it to "start" and see if the system loses power, then return on "run". you will have to check the system in sections to see which part is causing the issue though.

it could be the belt, or alt but the battery would most likely be dead by now, unless its the voltage regulator on the alternator allowing it to overcharge the battery thus damaging it.