There are some on-board diagnostics for single (or two for V-type engines) O2 sensors on most pre OBDII models, but they are not all inclusive.

Dual sensors - before and after the catalyst - are primarily intended to monitor catalyst performance.

The O2 sensor has nothing to do with starting since it doesn't generate a usable signal until it heats up to about 300 degrees C.

The O2 sensor on KE-equipped models may be indirectly checked by evaluating the EHA duty cycle, or the actual O2 sensor voltage signal pattern may be checked directly with a scope.

Duke