Actually, it is my brother’s Corvette.
When attempting to start the car on a few occassions, nothing happens except everything on the dashboard instrument panel lights up but absolutely no power is getting to the engine or starter. After waiting about 15 minutes, it starts up as if nothing ever happened.
Any ideas what could be wrong?
Does it make any noises, a slight clicking in the general engine area perhaps? Some Chevrolets from the same time had starting problems that I believe traced bad starters.
Have the battery checked as well, as batteries start to go bad, the car will have certain times where it just won’t want to start.
I don’t know if you can easily reach the starter on a 95 vette, but if you can, try giving it a good thump with a baseball bat. If the car starts, the starter is shot.
Of course, if it doesn’t start, it still could be the starter.
Do the lights go out while the starter is cranking? If so it might be the battery. If not then I’m leaning towards a starter problem.
Yeah, it sounds like it could be a bad starter, more specifically, the starter solenoid. The starter solenoid is basically a big electromagnet with a switch on it. When you turn the ignition, the starter solenoid is energized, which engages the starter pinion with the flywheel gear, and then closes a switch to power the starter motor itself. If you’re not hearing an audible “click” when you try to start the car, then it’s almost certainly the solenoid. On some cars, the solenoid is separately replaceable, on others it’s integrated with the starter motor.
The only other component which could be intermittant (if used) would be a starting relay. They’re common on Ford products and would cause the same problem as the OP, excepting in my own experience, when they fail, there’s no hope for self-healing after 15 minutes. If they’re not used at all on GM vehicles, then ignore this post. 
Now that I think of it, the Corvette is equipped with a PASS-Key Anti-Theft system.
A resistor embedded in the key is electronically “read” by a circuit in the ignition key lock. If the resistance is not the correct amount, even if you have the proper key, the car won’t start and you have to wait (4 minutes I think) before you can try another startup. This would definitely explain the time delay.
Does anyone know what is displayed if an improper startup has occurred?
On an 87 vette, you get no indication that the key did not read correctly. When you turn the key, nothing happens. If you try it again before the four minutes is up, the four-minute wait starts over.
Rubbing the key on you jeans usually cleans the contact enough that it will read correctly. I’ve been burned enough that I do it as a habit before trying to start the car.
The most common cause of the symptom described is a failing starter. Other causes include faulty ignition switch, faulty neutral saftey switch (automatic trans) or clutch starting switch (manual trans), faulty battery, and poor battery cable connections.