Our Magic Chef oven blew the element causing the lights in the house to go off for a brief moment. The lights came back on, but there was smoke coming from the oven. We turned the oven off and saw where the element had burned. The stove top will not work but the clock on it still works. We checked the circuit breaker and it will not flip back on. My question is, did we fry the stove and need to replace it or does the circuit breaker need to be replaced?

Unplug stove and reset breaker, if it doesn't reset, replace breaker.
If it does reset, and when plugged back it trips, something may still be shorted to ground in Oven, or other hot conductor.
Also replace the Element