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Dead Battery! Just happened to me yesterday. Had a brand new battery in there too. A Bosch. The positive terminal was loose as a result of the stereo shop we just bought a new radio from. It must have shorted out the battery. Take yours out and bring it in for a free test as Auto Zone.
Then get a new battery. By the way, the battery in my 94 requires you to remove the body panel in between the front wheel and the drivers door, the "gills", in order to get the battery out of the side of the car. good luck.......
Either your battery is totally dead or there is no electrical connection to your battery cables. Another possibility is a blown fusible link that goes to your ignition switch because almost all electrical devices get power from the ign sw.
You can tell the state of charge in your battery by measuring its terminal voltage under no load. 12.0 volts and below, discharged, charge your battery up with a battery charger. 12.9 volts and above, fully charged and linear in between these voltages. The dash voltmeter reads low if the engine is not running and it cannot be trusted.
A digital voltmeter is your friend when owning a Vette. If you don't have one, get one and keep it right in the car. As for the problem, try turning the headlights on as they bypass the ignition. If they don't come on it's either flat battery or a bad cable. If they do come on bright it still could be a bad cable or fusible link.