97 SC2 Shifting problem

Hi, I have a 97 SC2 with an automatic transmission. There is a shifting problem that is sort of weird. If the shifter is in park and I go to drive the car starts out fine but will not shift out of that gear. If I go from park to 3 and start off it shifts perfect. Here is the weird thing. If after starting off in 3 and then shift to D if goes into the last gear and works perfect. I can start-stop slow down speed up and it shift perfectly through all gears. It does not matter if it is hot or cold. But everytime I go from park or reverse to D I have to go through this put it in 3 and then to D. Could this be a shifter linkage adjustment problem? Thanks for any help.

ok so if you go from park to overdrive and drive the car, it wont shift out of first?

Yes. I know it sounds weird but that is exactly what it is doing.
Thanks

shift solenoid is about all i can come up with.