Electrical – Circuit breaker won’t turn back on after being turned off (not tripped)

Since neither the washer nor the dryer breaker are tripped, yet the main did trip and power to those circuits cannot be restored by resetting the main, I suspect either the circuit breakers, busbar section, or both have become damaged inside the panel -- this means the next steps involve turning the main breaker off and disassembling the branch circuit panel, looking for damage to the busbar tabs and breaker contact clips, as well as the breakers themselves.

If you're not comfortable doing this yourself, now's the time to get an electrician in; while you have them in, have them replace the misfit breaker with one of the correct type -- i.e. a THQL120 instead of the BR120 that was improperly fitted there, and install a blank over the gaping hole in the main panel.

(It's likely that the misfit breaker was making poor contact in the first place and just quit making contact with the busbar during whatever caused the main to trip. Replace it with a THQL120 and things should be good.)

Resistive heating elements (calrods), such as those in an electric oven, can break down and fail after a period of time due to deterioration of the internal insulation. When they do, the results can be quite spectacular, involving arcing from element and shell to the oven floor and a resulting fire when the arc ignites whatever grease deposits are present. However, this doesn't damage anything outside the oven, provided the fire itself stays inside the oven.

I would kill the power to the circuit and check the receptacle for any signs of damage (such as burn marks or metal spatter from arcing) anyway, though, just to be on the safe side.