Most likely culprit is the igniter.
When you turn the oven on it opens a gas valve allowing a small amount of gas to flow thru the pilot light. The igniter then lights the pilot and when the sensor determines the pilot is lit it opens th emain gas valve and the oven lights. If the igniter fails and doesn't light the pilot the sensor doesn't heat up and it shuts down the pilot and nothing works.
The igniter is usually accessable under the oven by removing the drawer. It has a single wire attached and looks like a short cigarette made of ceramic witha metal tip.
You didn't provide model number so I can't give you part number but if you look it up here you may be able to get one from Sears