The timer on my Kenmore stove works but doesn't beep when reaching 0:00

SOURCE: Kenmore self cleaning oven model 790.9520 : element stays on

sounds like it was in the preheat mode the cent to the cook mode so you can cook

SOURCE: My kenmore oven doesn't work.

ISOLATE MAINS POWER BEFORE OPENING PANELS
It sounds like you have acomponent blow, (stating the ob), what I would recommend is a visual inspection. remove panel on rear, have a good look at wiring and conponent that are visable. If no sign of black short on terminals it may be an element. The fault could be in the panel circuit but that would not produce enough smoke, a fan motor can an element and a electric switch, they use the two terminal type mounted usually on the chassis, if this appears burnt out replace with the same temp type. To go further you will need electrical knowledge, and a test meter. Let me know if you require further assistance.
John