Car refuses to start

My wife described to me a hard start issue with the 560SEL. I thought, here we go again! Last winter it would take a few cranks to turn it over in cold weather, replaced the OVP-- no go.

Per MBshop, a minor tune-up cured it.

So I tried it for myself and the symptoms are different. Turn the key, lights, fuel pumps come on, but it doesn’t start, no clicks etc. I jiggle the shifter and she starts right up.

First thing that comes to mind is the neutral safety switch, but I'm not sure yet if my wife moves the shifter. So I'm thinking bad starter (?) Not temperature dependent, but it seems to be time dependent.

Also, is the steering wheel supposed to be "locked"? I don't drive the big dog much anymore, so some of these details have escaped me.

TIA!

EDIT: Now that I think of it, this happened to me once during the summer. It seems the problem crops up more frequently.