Are you saying the car acts like it is in neutral even when in drive? Or is it in fixed 3rd gear (safe mode) in which case it will take off very slowly.

Is the check engine light on and/or upshift arrow (if your car has one) flashing? If so the codes set are likely to be revealing. If the trans fluid is not burnt, discolored or smelling bad, I'd bet on a technical issue such as a bad connection, etc.

Is there any history - replacement of PNP switch, removal of dash, accident, etc., that might contribute to something not having been put back properly then coming loose?

The shift interlock won't let you go out of park unless you have your foot on the brake.