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if i pull the negative cable off the battery and then reconnect, I get power (pulling about 11 volts). But as soon as I turn the key over to start, I hear a single click and everything goes dead.
11v and under is pretty low. You should have at least 11.8v Beyond that, it might be the starter. you can try tapping on the starter a few times with a hammer - sometimes that will work.
Don't know what you mean by "every thing goes dead" but try jumping the battery from another car and the "tapping of the starter" does work. Sometimes the brushes will sit on a "no contact spot" "they are hung up" and will not draw any current from the battery to make it turn over. Check the cable connection at the starter also. Plus, place a volt meter, set at 12 volts, between the battery posts and their respective connector. There should be a "zero" volt reading during cranking time(all of the time). There should be no voltage drop at the two battery posts and at the starter post. A VOM is a necessary item in a Corvette. Learn how to use it, and always keep it in the car. :seeya