The first thing to check is the fluid level, and you did that.
If the fluid is burnt smelling or discolored or you see particles in the fluid, it could be that the fluid is contaminated and needs to be flushed.
The third thing to check is the manual linkage, which can be done by disconnecting the cable from the transmission and shifting it by hand (use a partner to stand on the brakes and have the e-brake applied when you shift it into drive with you underneath...driver's side bottom contol cable). It can be disconnected by popping it off with a scewdriver. You can feel the stops with your hand (start in P and count the detents....P,R,OD,D,2,1). This makes sure that the column shifter and cable isn't selecting a position that is in between gears or slightly out one way or another.
The next thing to check is the control pressure. You need a gauge to do this check. The cheapest I've found is about $30. If the control pressure is low, either you have a bad pump or possibly a stuck regulator/booster valve. This pressure check lets you know for sure. When you have this pressure guage hooked up you have to do a stall test to get the pressure readings.
The next step would be to remove the valve body and clean it. This would be the first time that a mandatory fluid drain/refill would be required.
What gear does it redline at...which gear is slipping and what position is the shifter in?