[VetteVet]

Those wires are not fused so to burn like that they would have to be grounded some place.
When you turn the ignition key on you allow positive current from the battery directly to the starter and ignition coil.
The purple solenoid wire doesn't seem to be burned so I would rule out it being grounded.

Here is what I would do.

1. Disconnect the negative cable at the battery.
2.Connect a voltmeter, set to test continuity, between the burned wires and ground.
3. See if your reading is zero ohms. This would indicate a direct short to ground.
4. If zero or very low ohms, disconnect the + coil wire and read higher than 1.8 ohms.
5. If still zero disconnect the wire at the starter, outside terminal R, and repeat the
reading.
These two checks will eliminate the starter, and the coil/distributer circuits
6. If you still have zero ohms, then disconnect the firewall block and read the meter.
7. If still zero then your short is not in the cab, the starter, or the coil circuit, but the
wires in the engine bay which may be against a manifold or exhaust pipe.

Take these readings and get back with the results.