Yes, it could be the selector switch, which is on the left side of the transmission.
I had a similar problem on a car I had. At one point the shift lever had been jammed and forced which broke some internal parts. The previous owner had replaced the shift knob, but there was still damage in the actual shift selector. I often had to move the shift lever slightly out of (P) to get the car to start.
I replaced the whole shift selector.
Woody probably has some available and there are a few
on eBay.
I also found:
-The shift cable was not adjusted correctly.
-Transmission mounts were bad.