My 1962 Buick electra 225 wont start. When I turn the key the accesories come on but the engine wont start. it doesnt even try to start.

Check battery possible enough to light accessories but not start --then check for power to starter if good then possible ignition switch fail

Sounds like the relay in the starting motor circuit has failed, or a starting motor/solenoid problem - have them checked. This can also be caused by a problem in the ignition switch.