Bad Tranny or electrical

I just aquired a 93 z34. it had been parked fro about a year and a half and i am having serious tranny problems. the lady says that the last thing she had done to the car was a tranny rebuild and this problem remained. reverse works fine. To move foward i need to put the shifter in first or second gear and the car goes in to the same gear but im not sure if its 1st or 2nd. drive and over drive just slip as in neutral, but after i start moving in the 1st gear i can manually shift up to drive and it will shift(if im putting in to much throttle its slips until i let go and then it shifts.)it drives fine in drive as long as i stay over 10 mph or so, if i slow down to much it slips and i need to down shift manually again. I tried disconecting the conector that feeds all the shifter and solenoids and there it is able to start in drive but it still wont shift on its own.
Any ideas let me know, thank u

which tranny is it? the 60E?

Likely a 4T60E. If it is, and you have a pressure gauge, connect to the test port and check pressure in all ranges and PARK/NEUTRAL. Make sure the vacuum modulator is connectedand operating.