Sounds to me like your SLA (shift lever assembly) is mechanically faulty. I suppose the park/lock cable that goes to the ignition switch could be involved in this, but again, this is a mechanical issue in the SLA.
I do not own or drive vehicles with automatic transmissions - but I'm certain there is no physical linkage from the SLA to transmission, it is all electrical.

Yank the console out and get into the SLA and I think you will find a mechanical failure.