2003 Rangers will have electronically controlled transmissions, actually 1995 and up Ranger will.
So shifting is done by the computer via solenoids IN the transmission.
Check the 10 or 14 wire connector on the transmission to make sure it is plugged in correctly and tight
If possible get the Codes read, computer will set Transmission codes if there is a problem detected.
Computer may also put transmission in to "limp mode", harsh shifting, if the CEL(check engine light) comes on
Did you service the new/old transmission, drain fluid, change filter and refill?
If it sat for awhile it will sure need that