1987 Chevy Corvette Winter sitting

If the engine won't turn over at all, then are any of the electrical accessories working??? And do you hear any clicks when you turn the ignition key???

If you don't hear anything, and there's no power to anything else, then there's a problem in the circuit. First check your connections at the battery for loose/corroded cables, and all fuses/relays. Then you'll have to use a DVOM and trace both the power and ground circuits leading from the bat to the starter, bat to ground, ignition to starter.

If you do hear a clicking, and there's power to other electronics, then your bat can't hold a charge. You'll have to replace it.

And for future references, whenever you start a car every now and then (while you're storing a car for a length of time), you must let the engine run for at least 15-minutes. This gives the alternator enough time to charge the battery fully.

I'm assuming you have have voltage...I'm not going in depth, some common problems with vettes after storage; contaminated fuel, fuel goes bad after sitting also if the tank was not full water condensation form on the empty walls of tank also sounds dumb but rodents can nest in the under side and use your wire harness as nesting materials could be a bad starter thats unlikely could very well be a bad battery that has a bad cell because of you jump starting it always use a slow charger. Also the Vats system will prevent any cranking at all.Could also be the Ignition control module, Loose battery terminals.Coil.Or one of the many fusible links or grounds.Always start with the easiest then work your way to the hard stuff.Don't throw parts at it get a field service manual and start testing Pull codes. Carry on.