1953-1960 Classic Car Engines Troubleshooting Guide: Engine Starts But Won't Drive Car

Things to Look For:

Broken part in the drive line anywhere from clutch to rear axle shaft.
No oil or not enough oil in fluid coupling or torque converter.
Some defect in automatic transmission causes binding or dragging of clutches or slipping bands.
Engine develops only enough power to run itself due to: (a) extremely lean or rich mixture; (b) excessive engine friction; (c) throttle does not open; (d) very dirty air cleaner; (e) clogged exhaust system.
Oil in fluid coupling or torque converter is semi-solid due to zero temperature. This trouble is unlikely if the recommended oil is used.