The excessive cranking is because the fuel in the carburetor float bowl evaporates in a few days so the fuel pump has to move gas all the way from the tank, fill the carburetor before it can do its thing: supply fuel mixed with air to the engine.
The grinding sound is the starter motor not getting enough amperage. In other words, your battery is weak from all the cranking. Battery life is low in a car that is not driven regularly- a common issue with classic cars. That's why guys use battery tenders and such.
Use jumper cables from a running car and try starting it that way.
If that doesn't work use the old school techniques. An engine need three things to run:
- spark (at the right time)
- fuel (mixed with plenty of air)
- compression.
These are listed in order to check since the electrical is the least dependable and easiest to repair. Compression is rarely a problem especially over the short term.
It's unlikely that you have bad connections in all eight spark plugs at the same time so check the high tension coil wire first. You can connect an old spark plug to it and hold it against the engine block (ground) while someone turns the starter over. It should spark 4 times per engine revolution.
On the low voltage side does the coil have 12 volts with key start? Since you have a Pertronix points conversion it should have 12 volts with key-on as well. Is it connected property, positive and negative? The coil should be grounded from the distributor (points or electronic equivalent turn the ground on and off).
You can probably see where I'm going with this type of diagnosis. Check the basics first and work out from there.