Most capillary systems in the 70's (especially soda machines) didn't have a start-assist cap' plus I don't see one mounted on the compressor, So, since the compressor doesn't even start before the overload kicks out, the compressors either sticky, or just plain stuck, (locked-up)
You should try a 3-in-1 and see if it breaks the compressor free, then you
could try to reinstall the original start-run relay & overload, but I personally wouldn't bother as it's been stressed at this point & probably wouldn't be reliable anyway, take into consideration that this is a 30+ year old cooling deck & it may have just "retired" itself because of the compressor being bogged down with a sticky piston & drawing too much current, or now it's locked itself up.
Try a SUPCO 1/3-1/4 HP 3-in-1 booster/hard start unit, & if
that doesn't work, it's time for a new compressor.
Another passing thought is that maybe a loose connection, but you never stated what they ( the HVAC students) did to revive it...just curious.