It sounds like you might have a little short under your dash. The ding only works when the key is in the ignition. The second you pull it out, the ding should stop. The amplifier for the radio is also located right under the dash, near the tangle of ignition-controlled wires. Check there. Also, does the ding just stay on when the key is out or only when the key is in. If it stays on when the key is in only, I would say look at the wires that are switched on/off by the switch rather than those that always have power. It is also possible that the ignition switch is a bit messed up but since the radio isn't working, I look for the wiring issues.
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'Where's your common sense?' 'It left me when I was 5'