This happened to my DCS when the Hot Wire Relay went out. It isn't an expensive part, but finding someone that knows what needs to be replaced, and then can replace it is hard. My oven also did the opposite and continued to heat without shutting off, and it was once again the hot wire relay.

I don't have a solution but a follow up question... when your oven went out, did the broiler still work? My stovetop, grill plate and broiler all work fine, but my oven doesn't light. When it did work, it had the same delay, kawhooomp sound described above. The delay and noise became worse and worse until it stopped lighting altogether.