Kenmore 600 dryer won't start. Door switch?

I have an old Kenmore 600 series dryer, model#110.78632700. It is at least 10 years old, and could be a lot older.

It suddenly won't turn on. My first thought it might be the door switch, but the door switch is faulty but kind of works. Let me explain. If I open the dryer door and press w the metal tab on the upper right of the door, the interior light will come on, but it comes on unreliably. I have to fiddle with that metal tab, and after several attempts, the interior light will come on. My point is that the interior light does NOT come on reliably, but the interior light will come on.

So since the interior light does kind on unreliably, does this mean that the door switch is working? Or does this mean that the door switch has failed and needs replacement? Or is it something else?

I only ask this question because I don't want to order a new door switch and replace the door switch if there is no chance this will fix the problem - the problem that the dryer won't turn on anymore.

Oh, one last thing. Something specific happened when the dryer stopped starting. My wife was drying some sheets and stopped the dryer, so she could check the sheets. She did this mid-cycle. When she shot the front door and tried to start the dryer again, it would not start, and it has never started since then.