Crankshaft snags and loses resistance while cycling
It's not the cranks or bottom bracket (though it sounds like the BB might need replacing anyway) if the chain is moving normally.  The crank is fixed to the chain rings with bolts, so that can't slip.

It's much more likely that the ratchet mechanism in the rear hub is broken.  Older ones work on 2-4 small spring loaded "palls" that engage a ramped gear.  If the springs or the palls themselves rust and break, then the hub will no longer engage and you'll get that "no resistance" feeling.  The grinding you are feeling is probably bits of pall, spring, freehub body and possibly bearing moving around in the rear hub.  The lack of "tick-tick-tick" is because those palls are not being clicked into the gear by their springs.

Unfortunately, this probably means a new rear wheel.  The freehub body is probably ground down into pieces, and those pieces will have damaged the inside of the hub itself.   Technically, you could buy a new hub, and get your bike shop to lace that onto the existing rim, but it will probably be cheaper to just buy a whole rear wheel.