The previous machine, assuming it was another direct-drive unit, the most likely damage a small chain gotten loose out of the inner basket (escaped through a perf into the outer tub) would cause is getting into the pump and jamming it (and the motor from running). Replacing the pump is tres easy. Of course, I wasn't there, so could been something freakish happened.
The current machine, the serial number would be C645, which indicates manufacture in the 45th week of 1976 or 1986. Couldn't be 1976, direct-drive wasn't being produced then.
Do not find a off-balance cutout on the parts diagram.
Two auxiliary controls on the panel (temp & water level), so no separate speed switch.
Could be a flaky or broken lid switch, which comes into play during spin (and drain) periods. Easy fix. Investigation: Set the timer to spin, with the lid open, press the lid switch with a pencil or some such. Do you hear a faint click of the switch actuating? Does it run? In cases of extreme unbalance, the tub can bounce up and hit the lid switch under the top and break it.
Could be a flaky timer. Could be a bad motor. Both are available but toward the expensive (although a used motor could be had) so may not be worth doing depending on the 26-years-old machine's physical condition.
If the machine agitates OK, drains OK (neutral drain model), just dies/jams-up at spin, then could be a clutch or brake problem ... which also is fixable.