Whirlpool Ultimate Care II Washer won't advance through cycles.

Washer will fill, then stops. Barely audible buzzing sound heard until knob is reset. If manually moved to next step (agitation, rinse, etc.) it will work fine, then stops again at the end of that step with the audible buzzing again. There is no product information plate that I can locate on the machine for model number. If it is the timer, how can I determine the correct replacement? Thanks.