Put it in gear and give it some gas, see if speedometer works.
If it does rule out clutch and tranny.
More than likely it is the u-joint or front yoke or rear yoke.
That is the weak spot in the drive train.
Busted rear yoke
4 speed front yoke, u-joint, rear yoke

I had the same thing happen to me.
But I was not present.
I figured someone revved up the engine then slammed it in gear. It has a 1954 factory automatic tranny. Hydramatic.
But after reading elsewhere (last post on page 1 of thread) it does happen if you do not release the emergency brake completely.
The rear brakes are dragging down on the drive train and the first thing that snaps is the weakest spot in the drive train.
The u-joint or front yoke or rear yoke.
Basically its like your giving the engine gas with the tranny in gear and at the same time you have your foot on the brake pedal.

Sometimes the rear yoke gets hot and it snaps.
Could be that they never put U-Joint Locking Clips on the bolts. (only applies to 1941-54 U-Joint)
1929-40 U-joint illustration used 4 bolts & lock washers & nuts, scroll down on left side.
1941-54 U-Joint on right side.

1938 Chevrolet Shop Manual for All Passenger Cars and Trucks
UJ 1 Repair 1/2 ton bottom of page
UJ 2 Repair 1/2 ton
UJ 3 Repair 1/2 ton