2006 Automatic Tranny Shifter Issues

My daughter has her Tacoma out in south Texas, I'm in SC just to give you an idea of distances.

Tried searches, but this is a weird issue that I'm hoping someone has encountered.

She has had trouble getting the truck started due to what looks like the truck not registering that it might be in park. Also, might be an issue in regard to getting it to move once started since at times the transmission might not see that it is in "D" or "4".

Is there something either at shifter level or underneath that could be causing this issue? Once it is underway, it does not seem to be having a problem.

I'm wondering if this could be electrical as she broke the bolt on the negative terminal of the battery after i asked her to check the connections. I was thinking if the terminals aren't tight, the transmission computer might not be getting full voltage, therefore screwing up. Didn't go as I planned though when she broke the terminal bolt.