Your Kenmore gas range uses a glow bar igniter to ignite the burner and not a pilot light. Most likely the oven igniter is bad, but there is a possibility of the safety gas valve or oven thermostat to fail and cause the igniter to fail to operate too.
You did not indicate if the oven glow bar igniter is glowing red or not. Open the broiler drawer and visually check for a red glow when the oven is set to heat. If you see the oven igniter glowing red that would indicate the oven thermostat and the oven safety gas valve is OK and most likely the igniter is weak and needs to be replaced.
From a cold start, the igniter needs 30-60 seconds, with voltage applied, to reduce its electrical resistance enough to provide a minimum of 2.9 amps of current flow in the series circuit. This is the required current flow needed for the safety valve to open to supply gas to the burner. The glow bar should provide a steady current flow of between 3.2 to 3.6 amps flowing in the circuit. At that point the igniter temperature is between 1800 to 2500 degrees F. The igniter will remain energized at all times during burner operation. If the igniter glows red but does not draw at least 2.9 amps, the fault is usually with the igniter, not the valve.
I recommend calling a service technician to diagnose and repair your gas range.