I have encountered starters with stuck solenoid pistons after storage. I have found that if the starter can be activated one time, it will operate normally thereafter.
One method is what I call the Wakeup Call to the starter. The procedure is on page five of this document.
http://www.zr1specialist.com/HAT%20W...20problems.htm
The easy place to find the purple wire is on the clutch switch connector under the dash.
Another method is to vibrate the starter. The starter can be struck with a hammer. With a focused light look down next to the power brake booster. You will be able to see the corner of the coil pack. Under that is the starter. Use a 18" long 1/2" steel rod. Place it on the corner of the starter. Have a helper hold the ignition key to start. At the same time strike the steel rod.