There are a few likely reasons, but for the purposes of this post, we’re going to go with the most probable reason: your ignitor.
First, what is an ignitor you ask? Well, there is one in almost every gas oven today. The part most people recognize is the “glowbar”. As an electrical current flows through the hot (glowing) ignitor, a small piece of bimetal warps, sending millamps to open the gas valve. Your oven ignitor then ignites the gas. Yes, the valves could be your problem (I’m not guaranteeing anything), but the likelyhood is small.
If the ignitor is glowing slightly, it is still probably your issue. If it isn’t hot enough to warp the metal, your valve won’t open and your oven won’t turn on because of this one part of the equation. You may even be able to see a fracture or hairline crack on the glowbar of your ignitor.
If you own an ampmeter, you can diagnose this problem that way by measuring the amps that go from the ignitor to the valve. Different valves open at different amperages – look up your particular model. This part is just for your information, always make sure you use proper safety sense!
So, you either know or are guessing you have a bad ignitor, what now? Order a new one! (As always, I recommend Dey Distributing. Here’s a link to their ignitors for you: http://www.deyparts.net/catalog/range_oven_flat_oven_ignitors). They can’t be returned, so be careful on this next part… IF YOU TOUCH THE GLOWBAR IT WILL SHORTEN ITS LIFE. DON’T TOUCH …trust me, I know. They’ll come with wire nuts, so just attach the new ignitor in the same location as the old one.
Good luck – I’ll accept apple pies in exchange for the advice.