The service manuals (either factory, Haynes, Chiltons, etc.) are not online for free, but worth having one, even if you're not a mechanic, and can be bought at reasonable prices.
The "owner's manuals" are available for free, for C4s from 1993 to present, and the 93 is good for most things on C4s from 1984-92, anyway. You can get those owner manuals online at
www.corvette-world.com, look on the left column of its home page, under Corvette Articles for the entry for "Free Corvette Owners Manual (17)". Those are PDF and very handy, not to fix things, but to use things on your car.
Good luck. At least you have the car!
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