1993 Ford F350 transmission problem

Hi.
I have a 93 Ford, F-350, 4x4, 7.3 non-turbo, with automatic transmission, and 200K miles. 100K miles on transmission. When I start it up and put it in drive, it doesn't move. Then, just by pressing the O.D. Button, (overdrive off) trans kicks in and away we go. Run it up to speed, let off the throttle while turning O.D. Back on, and your in O.D.
As long as you don't over throttle, it drives just fine in O.D. But, if you over throttle, it kicks out (like you're in neutral). Switch the O.D. Back off and the trans kicks back in. Run it back up to speed, let off, turn O.D. Back on, and you're going again. Reverse works whether the O.D. Is on or off.

Any ideas?

P.S.- I've been driving the truck this way for about
5,000 miles.

Thank You, in advance, George (? Geowls)